29:
1962:
50:
1913:
819:
979:
1311:
935:
1881:
465:
1730:
1694:
777:
1806:
1828:
1406:
1278:
1074:
498:
1934:
1850:
1653:
1631:
1479:
1457:
1432:
1045:
1023:
1001:
874:
852:
740:
718:
697:
673:
651:
541:
519:
422:
400:
101:
73:
80:
2812:
87:
1359:
2807:
69:
2094:
159:
2118:
2313:
2183:
94:
2409:
170:
2462:
1990:
1314:
or smooth manifold is a differentiable manifold whose chart overlap functions are infinitely continuously differentiable.
2855:
2746:
120:
58:
2511:
1329:– A submanifold whose boundary equals its intersection with the boundary of the manifold into which it is embedded.
2494:
2103:
577:– The codimension of a submanifold is the dimension of the ambient space minus the dimension of the submanifold.
2865:
2860:
1340:
154:
54:
2706:
2113:
2691:
2414:
2188:
1768:– a section of a vector bundle. More specifically, a vector field can mean a section of the tangent bundle.
1608:
149:
1941:
2736:
2741:
2711:
2419:
2375:
2356:
2123:
2067:
1410:
1212:
2278:
2143:
1886:
2663:
2528:
2220:
2062:
1521:
1185:
782:
592:
39:
945:
2360:
2330:
2254:
2244:
2200:
2030:
1983:
1289:
1106:
1099:
908:
43:
2701:
2320:
2215:
2128:
2035:
1860:
1758:– a fiber bundle whose fibers are vector spaces and whose transition functions are linear maps.
1502:
1249:
431:
1699:
1663:
750:
2350:
2345:
1791:
142:
138:
1813:
1385:
630:
2681:
2619:
2467:
2171:
2161:
2133:
2108:
2018:
1256:
1052:
474:
8:
2819:
2501:
2379:
2364:
2293:
2052:
1143:
2792:
2761:
2716:
2613:
2484:
2288:
1976:
1919:
1835:
1638:
1616:
1530:
1464:
1442:
1417:
1129:
1030:
1008:
986:
859:
837:
725:
703:
682:
658:
636:
526:
504:
407:
385:
2298:
2696:
2676:
2671:
2578:
2489:
2303:
2283:
2138:
2077:
1854:
1540:
468:
1368:
2834:
2628:
2583:
2506:
2477:
2335:
2268:
2263:
2258:
2248:
2040:
2023:
1377:
1325:
877:
and identifying their boundaries. As the result we get a manifold without boundary.
601:
555:
350:
2777:
2686:
2516:
2472:
2238:
1241:
822:
611:
426:
2643:
2568:
2538:
2436:
2429:
2369:
2340:
2210:
2205:
2166:
1784:
1555:
1354:
625:
2849:
2829:
2653:
2648:
2633:
2623:
2573:
2550:
2424:
2384:
2325:
2273:
2072:
1754:
1581:
1110:
677:
583:
2756:
2751:
2593:
2560:
2533:
2441:
2082:
1764:
1216:
1157:
1119:
1083:
2599:
2588:
2545:
2446:
2047:
1779:
1511:
1245:
573:
1281:
manifold is a differentiable manifold whose chart overlap functions are
2824:
2782:
2608:
2521:
2153:
2057:
1968:
1590:
1199:
183:
2638:
2603:
2308:
2195:
1436:
1176:
888:
564:
28:
2802:
2797:
2787:
2178:
1999:
1559:– the vector bundle of tangent spaces on a differentiable manifold.
1488:
1236:
1204:
939:
134:
2394:
1937:
called the
Whitney sum of these vector bundles and denoted by
1599:
1358:– A smooth manifold is parallelizable if it admits a smooth
1656:
intersect transversally if at each point of intersection
1362:. This is equivalent to the tangent bundle being trivial.
1123:– the principal bundle of frames on a smooth manifold.
605:– the vector bundle of cotangent spaces on a manifold.
145:. The following three glossaries are closely related:
1944:
1922:
1889:
1863:
1838:
1816:
1794:
1702:
1666:
1641:
1619:
1467:
1445:
1420:
1388:
1292:
1259:
1055:
1033:
1011:
989:
948:
911:
862:
840:
785:
753:
728:
706:
685:
661:
639:
529:
507:
477:
434:
410:
388:
1956:
1928:
1907:
1875:
1844:
1822:
1800:
1724:
1688:
1647:
1625:
1473:
1451:
1426:
1400:
1305:
1272:
1068:
1039:
1017:
995:
973:
929:
868:
846:
813:
771:
734:
712:
691:
667:
645:
535:
513:
492:
459:
416:
394:
2847:
1515:– the image of a smooth embedding of a manifold.
1240:– A topological manifold is a locally Euclidean
855:with boundary, doubling is taking two copies of
70:"Glossary of differential geometry and topology"
1984:
1787:for vector bundles. Given two vector bundles
1482:and acts simply transitively on those fibers.
1534:– a two-dimensional manifold or submanifold.
57:. Unsourced material may be challenged and
1991:
1977:
180:denote a self-reference to this glossary.
160:Glossary of Riemannian and metric geometry
1544:– least length of a noncontractible loop.
121:Learn how and when to remove this message
1998:
1244:. (In Knowledge, a manifold need not be
1381:– A principal bundle is a fiber bundle
2848:
1972:
1571:of the tangent bundle. Also called a
1285:times continuously differentiable. A
1161:– A hypersurface is a submanifold of
1957:{\displaystyle \alpha \oplus \beta }
1783:– A Whitney sum is an analog of the
1732:generate the whole tangent space at
1203:– A lens space is a quotient of the
171:List of differential geometry topics
55:adding citations to reliable sources
22:
13:
1298:
14:
2877:
1211:+ 1)-sphere) by a free isometric
27:
471:on a manifold) that is closed:
186:
2031:Differentiable/Smooth manifold
1908:{\displaystyle B\to B\times B}
1893:
1719:
1713:
1683:
1677:
1392:
1341:Orientation of a vector bundle
968:
962:
921:
805:
763:
454:
435:
155:Glossary of algebraic topology
1:
1915:induces a vector bundle over
1460:that preserves the fibers of
814:{\displaystyle f^{-1}:N\to M}
974:{\displaystyle \pi ^{-1}(x)}
185:
150:Glossary of general topology
7:
2737:Classification of manifolds
1306:{\displaystyle C^{\infty }}
930:{\displaystyle \pi :E\to B}
403:with respect to an element
10:
2882:
2856:Glossaries of mathematics
2813:over commutative algebras
2770:
2729:
2662:
2559:
2455:
2402:
2393:
2229:
2152:
2091:
2011:
1876:{\displaystyle B\times B}
1026:is called the fiber over
460:{\displaystyle (C^{*},d)}
2529:Riemann curvature tensor
1857:is a vector bundle over
1725:{\displaystyle T_{p}(N)}
1689:{\displaystyle T_{p}(M)}
1186:Integration along fibers
772:{\displaystyle f:M\to N}
631:differentiable manifolds
198:
193:
1801:{\displaystyle \alpha }
1100:differentiable manifold
500:and the contraction of
2321:Manifold with boundary
2036:Differential structure
1958:
1930:
1909:
1877:
1846:
1824:
1823:{\displaystyle \beta }
1802:
1736:of the total manifold.
1726:
1690:
1649:
1627:
1475:
1453:
1428:
1402:
1401:{\displaystyle P\to B}
1307:
1274:
1070:
1041:
1019:
997:
975:
931:
870:
848:
815:
773:
736:
714:
693:
669:
647:
537:
515:
494:
461:
418:
396:
328:
323:
318:
313:
308:
303:
298:
293:
288:
283:
278:
273:
268:
263:
258:
253:
248:
243:
238:
233:
228:
223:
218:
213:
208:
203:
2866:Differential topology
2861:Differential geometry
1959:
1931:
1910:
1878:
1847:
1825:
1803:
1727:
1691:
1660:their tangent spaces
1650:
1628:
1476:
1454:
1429:
1403:
1308:
1275:
1273:{\displaystyle C^{k}}
1071:
1069:{\displaystyle E_{x}}
1042:
1020:
998:
976:
932:
904:– In a fiber bundle,
871:
849:
816:
774:
737:
715:
694:
670:
648:
538:
516:
495:
462:
419:
397:
143:differential topology
139:differential geometry
137:of terms specific to
2468:Covariant derivative
2019:Topological manifold
1942:
1920:
1887:
1861:
1836:
1814:
1792:
1772:
1747:
1700:
1664:
1639:
1617:
1548:
1495:
1465:
1443:
1418:
1386:
1347:
1333:
1318:
1290:
1257:
1229:
1192:
1169:
1150:
1136:
1053:
1031:
1009:
987:
946:
909:
895:
881:
860:
838:
783:
751:
726:
704:
683:
659:
637:
618:
548:
527:
505:
493:{\displaystyle dx=0}
475:
432:
408:
386:
357:
343:
51:improve this article
18:Mathematics glossary
2502:Exterior derivative
2104:Atiyah–Singer index
2053:Riemannian manifold
1883:. The diagonal map
1831:over the same base
1612:– Two submanifolds
833:– Given a manifold
425:is an element of a
187:Contents:
2808:Secondary calculus
2762:Singularity theory
2717:Parallel transport
2485:De Rham cohomology
2124:Generalized Stokes
1954:
1926:
1905:
1873:
1842:
1820:
1798:
1722:
1686:
1645:
1623:
1471:
1449:
1424:
1398:
1303:
1270:
1066:
1037:
1015:
993:
971:
927:
866:
844:
811:
769:
732:
710:
689:
665:
643:
533:
511:
490:
469:differential forms
467:(e.g., complex of
457:
414:
392:
2843:
2842:
2725:
2724:
2490:Differential form
2144:Whitney embedding
2078:Differential form
1929:{\displaystyle B}
1855:cartesian product
1845:{\displaystyle B}
1648:{\displaystyle N}
1626:{\displaystyle M}
1474:{\displaystyle P}
1452:{\displaystyle G}
1427:{\displaystyle P}
1409:together with an
1040:{\displaystyle x}
1018:{\displaystyle B}
996:{\displaystyle x}
869:{\displaystyle M}
847:{\displaystyle M}
735:{\displaystyle N}
713:{\displaystyle M}
692:{\displaystyle f}
668:{\displaystyle N}
646:{\displaystyle M}
536:{\displaystyle y}
514:{\displaystyle x}
417:{\displaystyle y}
395:{\displaystyle x}
131:
130:
123:
105:
2873:
2835:Stratified space
2793:Fréchet manifold
2507:Interior product
2400:
2399:
2097:
1993:
1986:
1979:
1970:
1969:
1963:
1961:
1960:
1955:
1935:
1933:
1932:
1927:
1914:
1912:
1911:
1906:
1882:
1880:
1879:
1874:
1851:
1849:
1848:
1843:
1829:
1827:
1826:
1821:
1807:
1805:
1804:
1799:
1731:
1729:
1728:
1723:
1712:
1711:
1695:
1693:
1692:
1687:
1676:
1675:
1654:
1652:
1651:
1646:
1632:
1630:
1629:
1624:
1480:
1478:
1477:
1472:
1458:
1456:
1455:
1450:
1433:
1431:
1430:
1425:
1407:
1405:
1404:
1399:
1378:Principal bundle
1326:Neat submanifold
1312:
1310:
1309:
1304:
1302:
1301:
1279:
1277:
1276:
1271:
1269:
1268:
1250:second-countable
1098:at a point of a
1075:
1073:
1072:
1067:
1065:
1064:
1048:, often denoted
1046:
1044:
1043:
1038:
1024:
1022:
1021:
1016:
1002:
1000:
999:
994:
980:
978:
977:
972:
961:
960:
936:
934:
933:
928:
875:
873:
872:
867:
853:
851:
850:
845:
823:smooth functions
820:
818:
817:
812:
798:
797:
779:and its inverse
778:
776:
775:
770:
741:
739:
738:
733:
719:
717:
716:
711:
698:
696:
695:
690:
674:
672:
671:
666:
652:
650:
649:
644:
602:Cotangent bundle
542:
540:
539:
534:
520:
518:
517:
512:
499:
497:
496:
491:
466:
464:
463:
458:
447:
446:
423:
421:
420:
415:
401:
399:
398:
393:
188:
126:
119:
115:
112:
106:
104:
63:
31:
23:
2881:
2880:
2876:
2875:
2874:
2872:
2871:
2870:
2846:
2845:
2844:
2839:
2778:Banach manifold
2771:Generalizations
2766:
2721:
2658:
2555:
2517:Ricci curvature
2473:Cotangent space
2451:
2389:
2231:
2225:
2184:Exponential map
2148:
2093:
2087:
2007:
1997:
1943:
1940:
1939:
1921:
1918:
1917:
1888:
1885:
1884:
1862:
1859:
1858:
1837:
1834:
1833:
1815:
1812:
1811:
1793:
1790:
1789:
1775:
1750:
1707:
1703:
1701:
1698:
1697:
1671:
1667:
1665:
1662:
1661:
1640:
1637:
1636:
1618:
1615:
1614:
1551:
1498:
1466:
1463:
1462:
1444:
1441:
1440:
1419:
1416:
1415:
1387:
1384:
1383:
1350:
1336:
1321:
1297:
1293:
1291:
1288:
1287:
1264:
1260:
1258:
1255:
1254:
1242:Hausdorff space
1232:
1223:
1195:
1172:
1153:
1139:
1060:
1056:
1054:
1051:
1050:
1032:
1029:
1028:
1010:
1007:
1006:
988:
985:
984:
953:
949:
947:
944:
943:
910:
907:
906:
898:
884:
861:
858:
857:
839:
836:
835:
790:
786:
784:
781:
780:
752:
749:
748:
727:
724:
723:
705:
702:
701:
684:
681:
680:
660:
657:
656:
638:
635:
634:
621:
612:Cotangent space
551:
528:
525:
524:
506:
503:
502:
476:
473:
472:
442:
438:
433:
430:
429:
427:cochain complex
409:
406:
405:
387:
384:
383:
360:
346:
340:
338:
337:
336:
335:
189:
127:
116:
110:
107:
64:
62:
48:
32:
19:
12:
11:
5:
2879:
2869:
2868:
2863:
2858:
2841:
2840:
2838:
2837:
2832:
2827:
2822:
2817:
2816:
2815:
2805:
2800:
2795:
2790:
2785:
2780:
2774:
2772:
2768:
2767:
2765:
2764:
2759:
2754:
2749:
2744:
2739:
2733:
2731:
2727:
2726:
2723:
2722:
2720:
2719:
2714:
2709:
2704:
2699:
2694:
2689:
2684:
2679:
2674:
2668:
2666:
2660:
2659:
2657:
2656:
2651:
2646:
2641:
2636:
2631:
2626:
2616:
2611:
2606:
2596:
2591:
2586:
2581:
2576:
2571:
2565:
2563:
2557:
2556:
2554:
2553:
2548:
2543:
2542:
2541:
2531:
2526:
2525:
2524:
2514:
2509:
2504:
2499:
2498:
2497:
2487:
2482:
2481:
2480:
2470:
2465:
2459:
2457:
2453:
2452:
2450:
2449:
2444:
2439:
2434:
2433:
2432:
2422:
2417:
2412:
2406:
2404:
2397:
2391:
2390:
2388:
2387:
2382:
2372:
2367:
2353:
2348:
2343:
2338:
2333:
2331:Parallelizable
2328:
2323:
2318:
2317:
2316:
2306:
2301:
2296:
2291:
2286:
2281:
2276:
2271:
2266:
2261:
2251:
2241:
2235:
2233:
2227:
2226:
2224:
2223:
2218:
2213:
2211:Lie derivative
2208:
2206:Integral curve
2203:
2198:
2193:
2192:
2191:
2181:
2176:
2175:
2174:
2167:Diffeomorphism
2164:
2158:
2156:
2150:
2149:
2147:
2146:
2141:
2136:
2131:
2126:
2121:
2116:
2111:
2106:
2100:
2098:
2089:
2088:
2086:
2085:
2080:
2075:
2070:
2065:
2060:
2055:
2050:
2045:
2044:
2043:
2038:
2028:
2027:
2026:
2015:
2013:
2012:Basic concepts
2009:
2008:
1996:
1995:
1988:
1981:
1973:
1967:
1966:
1953:
1950:
1947:
1925:
1904:
1901:
1898:
1895:
1892:
1872:
1869:
1866:
1841:
1819:
1797:
1785:direct product
1774:
1771:
1770:
1769:
1760:
1759:
1749:
1746:
1745:
1744:
1742:Trivialization
1738:
1737:
1721:
1718:
1715:
1710:
1706:
1685:
1682:
1679:
1674:
1670:
1644:
1622:
1609:Transversality
1604:
1603:
1595:
1594:
1586:
1585:
1577:
1576:
1561:
1560:
1556:Tangent bundle
1550:
1547:
1546:
1545:
1536:
1535:
1526:
1525:
1517:
1516:
1507:
1506:
1497:
1494:
1493:
1492:
1484:
1483:
1470:
1448:
1423:
1397:
1394:
1391:
1373:
1372:
1369:Poincaré lemma
1364:
1363:
1355:Parallelizable
1349:
1346:
1345:
1344:
1335:
1332:
1331:
1330:
1320:
1317:
1316:
1315:
1300:
1296:
1267:
1263:
1231:
1228:
1227:
1226:
1221:
1194:
1191:
1190:
1189:
1181:
1180:
1171:
1168:
1167:
1166:
1152:
1149:
1148:
1147:
1138:
1135:
1134:
1133:
1125:
1124:
1115:
1114:
1088:
1087:
1079:
1078:
1063:
1059:
1036:
1014:
992:
970:
967:
964:
959:
956:
952:
926:
923:
920:
917:
914:
897:
894:
893:
892:
883:
880:
879:
878:
865:
843:
827:
826:
810:
807:
804:
801:
796:
793:
789:
768:
765:
762:
759:
756:
745:diffeomorphism
731:
709:
688:
664:
642:
626:Diffeomorphism
620:
617:
616:
615:
607:
606:
597:
596:
588:
587:
579:
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196:
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174:
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129:
128:
35:
33:
26:
17:
9:
6:
4:
3:
2:
2878:
2867:
2864:
2862:
2859:
2857:
2854:
2853:
2851:
2836:
2833:
2831:
2830:Supermanifold
2828:
2826:
2823:
2821:
2818:
2814:
2811:
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2806:
2804:
2801:
2799:
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2567:
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2564:
2562:
2558:
2552:
2551:Wedge product
2549:
2547:
2544:
2540:
2537:
2536:
2535:
2532:
2530:
2527:
2523:
2520:
2519:
2518:
2515:
2513:
2510:
2508:
2505:
2503:
2500:
2496:
2495:Vector-valued
2493:
2492:
2491:
2488:
2486:
2483:
2479:
2476:
2475:
2474:
2471:
2469:
2466:
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2454:
2448:
2445:
2443:
2440:
2438:
2435:
2431:
2428:
2427:
2426:
2425:Tangent space
2423:
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2219:
2217:
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2209:
2207:
2204:
2202:
2199:
2197:
2194:
2190:
2189:in Lie theory
2187:
2186:
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2110:
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2101:
2099:
2096:
2092:Main results
2090:
2084:
2081:
2079:
2076:
2074:
2073:Tangent space
2071:
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2061:
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2025:
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2020:
2017:
2016:
2014:
2010:
2005:
2001:
1994:
1989:
1987:
1982:
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1964:
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1777:
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1757:
1756:
1755:Vector bundle
1752:
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1743:
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1672:
1668:
1659:
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1597:
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1582:Tangent space
1579:
1578:
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1570:
1566:
1565:Tangent field
1563:
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1127:
1126:
1122:
1121:
1117:
1116:
1113:at the point.
1112:
1111:tangent space
1108:
1104:
1101:
1097:
1093:
1090:
1089:
1086:
1085:
1081:
1080:
1076:
1061:
1057:
1047:
1034:
1025:
1012:
1003:
990:
981:
965:
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941:
937:
924:
918:
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854:
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832:
829:
828:
824:
808:
802:
799:
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791:
787:
766:
760:
757:
754:
746:
742:
729:
720:
707:
686:
679:
678:bijective map
675:
662:
653:
640:
632:
628:
627:
623:
622:
614:
613:
609:
608:
604:
603:
599:
598:
595:
594:
590:
589:
586:
585:
584:Connected sum
581:
580:
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575:
571:
570:
567:
566:
562:
561:
558:
557:
553:
552:
543:
530:
521:
508:
487:
484:
481:
478:
470:
451:
448:
443:
439:
428:
424:
411:
402:
389:
381:
380:basic element
377:
376:basic element
374:
373:
369:
365:
362:
361:
353:
352:
348:
347:
341:
334:
330:
327:
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317:
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307:
305:
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161:
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148:
147:
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144:
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136:
125:
122:
114:
111:December 2009
103:
100:
96:
93:
89:
86:
82:
79:
75:
72: –
71:
67:
66:Find sources:
60:
56:
52:
46:
45:
41:
36:This article
34:
30:
25:
24:
21:
16:
2757:Moving frame
2752:Morse theory
2742:Gauge theory
2534:Tensor field
2463:Closed/Exact
2442:Vector field
2410:Distribution
2351:Hypercomplex
2346:Quaternionic
2083:Vector field
2041:Smooth atlas
2003:
1938:
1916:
1832:
1810:
1788:
1778:
1765:Vector field
1763:
1753:
1741:
1733:
1657:
1635:
1613:
1607:
1598:
1589:
1580:
1573:vector field
1572:
1568:
1564:
1554:
1539:
1529:
1520:
1510:
1501:
1487:
1461:
1439:
1414:
1382:
1376:
1367:
1360:global frame
1353:
1339:
1324:
1286:
1282:
1253:
1235:
1217:
1208:
1198:
1184:
1175:
1162:
1158:Hypersurface
1156:
1142:
1128:
1120:Frame bundle
1118:
1102:
1095:
1091:
1084:Fiber bundle
1082:
1049:
1027:
1005:
1004:in the base
983:
942:
905:
901:
887:
856:
834:
830:
744:
743:is called a
722:
700:
655:
633:
629:– Given two
624:
610:
600:
591:
582:
572:
563:
554:
523:
501:
404:
382:
379:
375:
368:fiber bundle
367:
363:
349:
339:
333:
177:
175:
165:
132:
117:
108:
98:
91:
84:
77:
65:
49:Please help
37:
20:
15:
2702:Levi-Civita
2692:Generalized
2664:Connections
2614:Lie algebra
2546:Volume form
2447:Vector flow
2420:Pushforward
2415:Lie bracket
2314:Lie algebra
2279:G-structure
2068:Pushforward
2048:Submanifold
1780:Whitney sum
1512:Submanifold
1246:paracompact
1163:codimension
982:of a point
574:Codimension
2850:Categories
2825:Stratifold
2783:Diffeology
2579:Associated
2380:Symplectic
2365:Riemannian
2294:Hyperbolic
2221:Submersion
2129:Hopf–Rinow
2063:Submersion
2058:Smooth map
1591:Thom space
1522:Submersion
1200:Lens space
747:– if both
593:Connection
166:See also:
133:This is a
81:newspapers
2707:Principal
2682:Ehresmann
2639:Subbundle
2629:Principal
2604:Fibration
2584:Cotangent
2456:Covectors
2309:Lie group
2289:Hermitian
2232:manifolds
2201:Immersion
2196:Foliation
2134:Noether's
2119:Frobenius
2114:De Rham's
2109:Darboux's
2000:Manifolds
1952:β
1949:⊕
1946:α
1900:×
1894:→
1868:×
1818:β
1796:α
1437:Lie group
1393:→
1299:∞
1177:Immersion
955:−
951:π
922:→
913:π
889:Embedding
806:→
792:−
764:→
565:Cobordism
444:∗
176:Words in
38:does not
2803:Orbifold
2798:K-theory
2788:Diffiety
2512:Pullback
2326:Oriented
2304:Kenmotsu
2284:Hadamard
2230:Types of
2179:Geodesic
2004:Glossary
1489:Pullback
1237:Manifold
1205:3-sphere
940:preimage
831:Doubling
544:is zero.
135:glossary
2747:History
2730:Related
2644:Tangent
2622:)
2602:)
2569:Adjoint
2561:Bundles
2539:density
2437:Torsion
2403:Vectors
2395:Tensors
2378:)
2363:)
2359:,
2357:Pseudo−
2336:Poisson
2269:Finsler
2264:Fibered
2259:Contact
2257:)
2249:Complex
2247:)
2216:Section
1569:section
1541:Systole
1531:Surface
1503:Section
1109:of the
178:italics
95:scholar
59:removed
44:sources
2712:Vector
2697:Koszul
2677:Cartan
2672:Affine
2654:Vector
2649:Tensor
2634:Spinor
2624:Normal
2620:Stable
2574:Affine
2478:bundle
2430:bundle
2376:Almost
2299:Kähler
2255:Almost
2245:Almost
2239:Closed
2139:Sard's
2095:(list)
1853:their
1411:action
1213:action
1207:(or (2
366:– see
364:Bundle
97:
90:
83:
76:
68:
2820:Sheaf
2594:Fiber
2370:Rizza
2341:Prime
2172:Local
2162:Curve
2024:Atlas
1600:Torus
1435:by a
1252:.) A
1144:Genus
1107:basis
1105:is a
1096:frame
1092:Frame
902:Fiber
699:from
556:Chart
351:Atlas
102:JSTOR
88:books
2687:Form
2589:Dual
2522:flow
2385:Tame
2361:Sub−
2274:Flat
2154:Maps
1809:and
1696:and
1634:and
1567:– a
1165:one.
1130:Flow
1094:– A
938:the
821:are
676:, a
654:and
378:– A
141:and
74:news
42:any
40:cite
2609:Jet
1413:on
1248:or
1215:of
721:to
522:by
199:0–9
194:Top
53:by
2852::
2600:Co
1220:–
2618:(
2598:(
2374:(
2355:(
2253:(
2243:(
2006:)
2002:(
1992:e
1985:t
1978:v
1965:.
1924:B
1903:B
1897:B
1891:B
1871:B
1865:B
1840:B
1773:W
1748:V
1734:p
1720:)
1717:N
1714:(
1709:p
1705:T
1684:)
1681:M
1678:(
1673:p
1669:T
1658:p
1643:N
1621:M
1575:.
1549:T
1496:S
1469:P
1447:G
1422:P
1396:B
1390:P
1348:P
1334:O
1319:N
1295:C
1283:k
1266:k
1262:C
1230:M
1225:.
1222:k
1218:Z
1209:n
1193:L
1170:I
1151:H
1137:G
1103:M
1077:.
1062:x
1058:E
1035:x
1013:B
991:x
969:)
966:x
963:(
958:1
925:B
919:E
916::
896:F
882:E
864:M
842:M
825:.
809:M
803:N
800::
795:1
788:f
767:N
761:M
758::
755:f
730:N
708:M
687:f
663:N
641:M
619:D
549:C
531:y
509:x
488:0
485:=
482:x
479:d
455:)
452:d
449:,
440:C
436:(
412:y
390:x
370:.
358:B
344:A
329:Z
324:Y
319:X
314:W
309:V
304:U
299:T
294:S
289:R
284:Q
279:P
274:O
269:N
264:M
259:L
254:K
249:J
244:I
239:H
234:G
229:F
224:E
219:D
214:C
209:B
204:A
162:.
124:)
118:(
113:)
109:(
99:·
92:·
85:·
78:·
61:.
47:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
