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Ambient space (mathematics)

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Schilders, W. H. A.; ter Maten, E. J. W.; Ciarlet, Philippe G. (2005).
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may be studied in isolation โ€”in which case the ambient space of
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lines never intersect." This is true if the ambient space is
582: 30:"Ambient space" redirects here. Not to be confused with 496: 467: 434: 405: 372: 352: 317: 285: 265: 230: 204: 184: 158: 610: 511: 482: 449: 420: 387: 358: 338: 300: 271: 251: 210: 190: 170: 693: 218:, or it may be studied as an object embedded in 64:but its sources remain unclear because it lacks 490:are different from the geometric properties of 146:along with the object itself. For example, a 676: 308:, or as an object embedded in 2-dimensional 683: 669: 499: 470: 437: 408: 375: 323: 288: 236: 111:Three examples of different geometries: 95:Learn how and when to remove this message 106: 605: 14: 694: 613:Chaotic Transport in Dynamical Systems 585:Numerical Methods in Electromagnetics 635: 617:. Berlin: Springer. pp. 209ff. 428:, but false if the ambient space is 346:โ€”in which case the ambient space of 259:โ€”in which case the ambient space of 36: 24: 576: 339:{\displaystyle (\mathbb {H} ^{2})} 252:{\displaystyle (\mathbb {R} ^{2})} 25: 723: 639: 512:{\displaystyle \mathbb {H} ^{2}} 483:{\displaystyle \mathbb {R} ^{2}} 450:{\displaystyle \mathbb {H} ^{2}} 421:{\displaystyle \mathbb {R} ^{2}} 388:{\displaystyle \mathbb {H} ^{2}} 301:{\displaystyle \mathbb {R} ^{2}} 41: 27:The space surrounding an object 333: 318: 246: 231: 165: 159: 13: 1: 655:. You can help Knowledge by 587:. Vol. Special Volume. 7: 526: 142:is the space surrounding a 10: 728: 634: 32:Ambient space (psychology) 29: 523:of their ambient space. 50:This article includes a 79:more precise citations. 513: 484: 451: 422: 389: 360: 340: 302: 273: 253: 212: 192: 172: 123: 514: 485: 452: 423: 390: 361: 341: 303: 274: 254: 213: 193: 173: 110: 561:Riemannian manifolds 494: 465: 459:geometric properties 432: 403: 370: 350: 315: 283: 263: 228: 202: 182: 156: 533:Configuration space 171:{\displaystyle (l)} 144:mathematical object 591:. pp. 120ff. 519:. All spaces are 509: 480: 447: 418: 385: 356: 336: 298: 269: 249: 208: 188: 168: 124: 52:list of references 664: 663: 571:Differential form 359:{\displaystyle l} 272:{\displaystyle l} 211:{\displaystyle l} 191:{\displaystyle l} 105: 104: 97: 16:(Redirected from 719: 685: 678: 671: 649:geometry-related 643: 636: 628: 616: 607:Wiggins, Stephen 602: 547:ambient manifold 518: 516: 515: 510: 508: 507: 502: 489: 487: 486: 481: 479: 478: 473: 456: 454: 453: 448: 446: 445: 440: 427: 425: 424: 419: 417: 416: 411: 394: 392: 391: 386: 384: 383: 378: 365: 363: 362: 357: 345: 343: 342: 337: 332: 331: 326: 310:hyperbolic space 307: 305: 304: 299: 297: 296: 291: 278: 276: 275: 270: 258: 256: 255: 250: 245: 244: 239: 217: 215: 214: 209: 197: 195: 194: 189: 177: 175: 174: 169: 130:, especially in 100: 93: 89: 86: 80: 75:this article by 66:inline citations 45: 44: 37: 21: 727: 726: 722: 721: 720: 718: 717: 716: 692: 691: 690: 689: 632: 625: 599: 579: 577:Further reading 566:Ricci curvature 538:Geometric space 529: 503: 498: 497: 495: 492: 491: 474: 469: 468: 466: 463: 462: 441: 436: 435: 433: 430: 429: 412: 407: 406: 404: 401: 400: 379: 374: 373: 371: 368: 367: 351: 348: 347: 327: 322: 321: 316: 313: 312: 292: 287: 286: 284: 281: 280: 264: 261: 260: 240: 235: 234: 229: 226: 225: 223:Euclidean space 203: 200: 199: 183: 180: 179: 157: 154: 153: 101: 90: 84: 81: 70: 56:related reading 46: 42: 35: 28: 23: 22: 15: 12: 11: 5: 725: 715: 714: 712:Geometry stubs 709: 704: 688: 687: 680: 673: 665: 662: 661: 644: 630: 629: 623: 603: 597: 578: 575: 574: 573: 568: 563: 558: 549: 540: 535: 528: 525: 506: 501: 477: 472: 457:, because the 444: 439: 415: 410: 382: 377: 355: 335: 330: 325: 320: 295: 290: 268: 248: 243: 238: 233: 207: 187: 167: 164: 161: 103: 102: 60:external links 49: 47: 40: 26: 9: 6: 4: 3: 2: 724: 713: 710: 708: 705: 703: 700: 699: 697: 686: 681: 679: 674: 672: 667: 666: 660: 658: 654: 651:article is a 650: 645: 642: 638: 637: 633: 626: 624:3-540-97522-5 620: 615: 614: 608: 604: 600: 598:0-444-51375-2 594: 590: 586: 581: 580: 572: 569: 567: 564: 562: 559: 557: 556:Hypersurfaces 553: 550: 548: 544: 541: 539: 536: 534: 531: 530: 524: 522: 504: 475: 460: 442: 413: 398: 380: 353: 328: 311: 293: 266: 241: 224: 221: 220:2-dimensional 205: 185: 162: 152: 149: 148:1-dimensional 145: 141: 140:ambient space 137: 133: 129: 122: 118: 114: 109: 99: 96: 88: 78: 74: 68: 67: 61: 57: 53: 48: 39: 38: 33: 19: 18:Ambient space 657:expanding it 646: 631: 612: 584: 552:Submanifolds 139: 125: 91: 82: 71:Please help 63: 128:mathematics 77:introducing 696:Categories 121:hyperbolic 117:elliptical 113:Euclidean 707:Topology 702:Geometry 609:(1992). 589:Elsevier 543:Manifold 527:See also 397:Parallel 136:topology 132:geometry 85:May 2024 521:subsets 73:improve 621:  595:  119:, and 647:This 138:, an 58:, or 653:stub 619:ISBN 593:ISBN 554:and 545:and 151:line 134:and 461:of 366:is 279:is 198:is 126:In 698:: 115:, 62:, 54:, 684:e 677:t 670:v 659:. 627:. 601:. 505:2 500:H 476:2 471:R 443:2 438:H 414:2 409:R 381:2 376:H 354:l 334:) 329:2 324:H 319:( 294:2 289:R 267:l 247:) 242:2 237:R 232:( 206:l 186:l 166:) 163:l 160:( 98:) 92:( 87:) 83:( 69:. 34:. 20:)

Index

Ambient space
Ambient space (psychology)
list of references
related reading
external links
inline citations
improve
introducing
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Euclidean
elliptical
hyperbolic
mathematics
geometry
topology
mathematical object
1-dimensional
line
2-dimensional
Euclidean space
hyperbolic space
Parallel
geometric properties
subsets
Configuration space
Geometric space
Manifold
ambient manifold
Submanifolds

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