Knowledge

Wiedersehen pair

Source πŸ“

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Weinstein, Alan (1974-01-01). "On the volume of manifolds all of whose geodesics are closed".
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Kazdan, Jerry L. (1982). "An isoperimetric inequality and Wiedersehen manifolds".
208: 131: 90: 445: 320: 170: 162: 259: 488: 350: 341: 324: 312: 304: 239: 154: 124: 48: 433: 158: 86: 28: 415: 396: 203:. Berlin, Heidelberg: Springer Berlin Heidelberg. p. 236–242. 143: 63: 134:
term meaning "seeing again". As it turns out, in each dimension
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Berger, Marcel (1978). "Blaschke's Conjecture for Sphere".
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For example, on an ordinary sphere where the geodesics are
365:. New York: Cambridge University Press. pp. 328–329. 386: 47:
on a (usually, but not necessarily, two-dimensional)
153:, this result was established by combined works of 325:"Odd-dimensional wiedersehen manifolds are spheres" 89:, the Wiedersehen pairs are exactly the pairs of 486: 275:"Summary of progress on the Blaschke conjecture" 469: 201:Manifolds all of whose Geodesics are Closed 476: 462: 363:Riemannian geometry: a modern introduction 319: 241:Seminar on Differential Geometry. (AM-102) 340: 290: 225: 108:) belongs to a Wiedersehen pair, then ( 14: 487: 357: 237: 231:Vorlesung ΓΌber Differentialgeometrie I 198: 406: 387: 138:the only Wiedersehen manifold (up to 428: 120:. The concept was introduced by the 24: 25: 521: 380: 272: 432: 293:Journal of Differential Geometry 187:Cut locus (Riemannian manifold) 244:. Princeton University Press. 13: 1: 192: 39:is a pair of distinct points 448:. You can help Knowledge by 209:10.1007/978-3-642-61876-5_13 142:) is the standard Euclidean 7: 180: 10: 526: 427: 233:. Berlin: Springer-Verlag. 505:Riemannian geometry stubs 149:. Initially known as the 31:—specifically, in 444:-related article is a 342:10.4310/jdg/1214435386 305:10.4310/jdg/1214432547 411:"Wiedersehen surface" 96:If every point of an 329:J. Differential Geom 118:Wiedersehen manifold 74:, and the same with 70:also passes through 18:Wiedersehen manifold 495:Riemannian geometry 442:Riemannian geometry 151:Blaschke conjecture 130:and comes from the 52:Riemannian manifold 33:Riemannian geometry 408:Weisstein, Eric W. 392:"Wiedersehen pair" 389:Weisstein, Eric W. 116:) is said to be a 62:) such that every 457: 456: 273:McKay, Benjamin. 251:978-0-691-08268-4 227:Blaschke, Wilhelm 218:978-3-642-61878-9 16:(Redirected from 517: 478: 471: 464: 436: 429: 421: 420: 402: 401: 376: 354: 344: 316: 287: 285: 284: 279: 269: 267: 266: 234: 222: 128:Wilhelm Blaschke 122:Austro-Hungarian 91:antipodal points 37:Wiedersehen pair 21: 525: 524: 520: 519: 518: 516: 515: 514: 485: 484: 483: 482: 425: 383: 373: 282: 280: 277: 264: 262: 252: 219: 195: 183: 23: 22: 15: 12: 11: 5: 523: 513: 512: 507: 502: 497: 481: 480: 473: 466: 458: 455: 454: 437: 423: 422: 403: 382: 381:External links 379: 378: 377: 371: 355: 317: 288: 270: 260:j.ctt1bd6kkq.9 250: 235: 223: 217: 194: 191: 190: 189: 182: 179: 82:interchanged. 9: 6: 4: 3: 2: 522: 511: 508: 506: 503: 501: 498: 496: 493: 492: 490: 479: 474: 472: 467: 465: 460: 459: 453: 451: 447: 443: 438: 435: 431: 430: 426: 418: 417: 412: 409: 404: 399: 398: 393: 390: 385: 384: 374: 372:0-521-61954-8 368: 364: 360: 359:Chavel, Isaac 356: 352: 348: 343: 338: 334: 330: 326: 322: 318: 314: 310: 306: 302: 298: 294: 289: 276: 271: 261: 257: 253: 247: 243: 242: 236: 232: 228: 224: 220: 214: 210: 206: 202: 197: 196: 188: 185: 184: 178: 176: 172: 168: 164: 160: 156: 152: 148: 146: 141: 137: 133: 129: 126: 125:mathematician 123: 119: 115: 111: 107: 103: 99: 94: 92: 88: 87:great circles 83: 81: 77: 73: 69: 65: 61: 57: 53: 50: 46: 42: 38: 34: 30: 19: 450:expanding it 439: 424: 414: 395: 362: 335:(1): 91–96. 332: 328: 296: 292: 281:. Retrieved 263:. Retrieved 240: 230: 200: 174: 166: 150: 144: 135: 117: 113: 109: 105: 101: 95: 84: 79: 75: 71: 67: 59: 55: 44: 40: 36: 26: 29:mathematics 489:Categories 321:C. T. Yang 283:2024-01-29 265:2024-01-29 193:References 165:(for even 100:manifold ( 510:Manifolds 500:Equations 416:MathWorld 397:MathWorld 351:0022-040X 313:0022-040X 163:Weinstein 35:—a 361:(2006). 323:(1980). 229:(1921). 181:See also 140:isometry 98:oriented 66:through 64:geodesic 169:), and 147:-sphere 112:,  104:,  58:,  49:compact 369:  349:  311:  258:  248:  215:  159:Kazdan 155:Berger 132:German 440:This 299:(4). 278:(PDF) 256:JSTOR 173:(odd 446:stub 367:ISBN 347:ISSN 309:ISSN 246:ISBN 213:ISBN 171:Yang 78:and 43:and 337:doi 301:doi 205:doi 177:). 27:In 491:: 413:. 394:. 345:. 333:15 331:. 327:. 307:. 295:. 254:. 211:. 161:, 157:, 93:. 477:e 470:t 463:v 452:. 419:. 400:. 375:. 353:. 339:: 315:. 303:: 297:9 286:. 268:. 221:. 207:: 175:n 167:n 145:n 136:n 114:g 110:M 106:g 102:M 80:y 76:x 72:y 68:x 60:g 56:M 54:( 45:y 41:x 20:)

Index

Wiedersehen manifold
mathematics
Riemannian geometry
compact
Riemannian manifold
geodesic
great circles
antipodal points
oriented
Austro-Hungarian
mathematician
Wilhelm Blaschke
German
isometry
n-sphere
Berger
Kazdan
Weinstein
Yang
Cut locus (Riemannian manifold)
doi
10.1007/978-3-642-61876-5_13
ISBN
978-3-642-61878-9
Blaschke, Wilhelm
Seminar on Differential Geometry. (AM-102)
ISBN
978-0-691-08268-4
JSTOR
j.ctt1bd6kkq.9

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