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Berger M. — A Panoramic View of Riemannian Geometry
Berger M. — A Panoramic View of Riemannian Geometry



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Название: A Panoramic View of Riemannian Geometry

Автор: Berger M.

Аннотация:

In his latest book A Panoramic View of Riemannian Geometry, Marcel Berger does a remarkable job giving an in-depth survey ranging over almost the full spectrum of Riemannian geometry, furnishing the reader with some of the most exciting and elegant topics from classical to modern, and from local to global Riemannian geometry.
The reader will find that, unlike many other books on Riemannian geometry, the style of this 15-chapter 824-page manuscript is quite unique. The author does not follow the traditional definition-theorem-proof approach; instead, he only motivates and presents, without detailed proofs, the best possible results in many areas known to date, thereby providing interested readers with a valuable source and efficient means for learning about the latest advances. Additionally, throughout the book, open problems are introduced and discussed as soon as they can be stated.

The organization of the material in this book also distinguishes itself from many of its peers - as Berger says, "in our division into chapters, necessarily arbitrary, we did not follow any logical or historical order. We have tried to follow certain naturalness and simplicity."


Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 872

Добавлена в каталог: 12.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\eta$ invariant      399 453 547
Abrahamov, A.A.      742
Abresch — Meyer theorem      300
Abresch, Uwe      200 286 300 587 589 598 603 609 626 637 640 650 656
Absolute calculus      723 730
Acceleration      13 725
Accola, Robert D.M.      354
Action-angle coordinates      464
Adjoint of exterior derivative      690
Ahlfors, Lars V.      157
Aicardi, Francesca      29
Akutagawa, Kazuo      628
Alekseevskii, D.V.      671
Alexander, Stephanie B.      702
Alexandrov space      309 625 660 704
Alexandrov, Aleksandr Danilovich      65 134—139 237 282 704
Alexandrov’s conjecture      65
Algorithmic computability      566
Allendoerfer, Carl B.      735 738 739
Alling, Norman L.      317
Allof — Wallach manifold      541 604
Aloft, Simon      605
Alvarez Paiva, Juan Carlos      709
Ambrose problem      237 273 309 730
Ambrose, W.      236 237 309 669 730
Amenable group      544
Amords, J.      681 701
Analytic real      51
Anderson, Michael T.      179 236 291 444 528 529 537 548 550 551 559 561 595 599 621 650 651 655 656 660 661 702 703
Andrews, Ben      20 28
angle      3
Anosov, D.V.      491 498 504
Antipode      520
Appell, Paul      220
Appolonius of Perga      256
Aranson, S.Kh.      498
Aravinda, C.S.      597
Arconstanzo, Marc      702
Arithmetic hyperbolic manifold      317
Arnol’d, Vladimir I.      21 29 44 79 144 166 220 263 305 495 498 711
Arnoux, Pierre      5 7 9 112
Ashbaugh, Mark S.      94
Aspherical      369
Assay, non-destructive      97
Astronomy      3
Asymptote      613
Asymptotic line      79
Atiyah — Singer index theorem      699
Atiyah, Michael F.      428 452 453 698 699
Atomann, Bernd      153
Aubin, Thierry      349 399 555 561
Audoly, Basile      145
Avakumovic, V.      398 428
Avez, A.      498
Axiom Euclidean      115
Axiom of mobility      276 314
Axis of a hyperbolic glide      447
Babenko, Ivan K.      372—374 687 693
Babic, Vasilii M.      432
Baily, W.L.      703
Balian, R.      90 104 429 431
Ball bearings      20
Ballmann, Werner      278 280 491 497 503 504 509 632 635—638 687 703
Bandle, Catherine      426
Bangert — Franks — Hingston theorem      494
Bangert, Victor      372 460 470 494 495
Bar, Christian      696
Baston, Robert J.      681
Bavard, Christophe      353 359 640
Bazaikin manifold      605
Bazarkin, Ya.V.      605
Beauville, Arnaud      365 680
Beem, John K.      710
Bemelmans, Josef      656
Ben-Av, Radel      562
Bending      145
Benedetti, Riccardo      196 201 545
Benguria, Rafael D.      94
Benjamini, Itai      688
Benoist, Yves      524 710
Berard Bergery, Lionel      373 556 604
Berard Bergery/Salamon twistor space      676
Berard, Pierre H.      83 88 91 92 96 101 102 104 111 343 344 399 407 409 410 425 426 432 441 442 622 710 735
Berestovskij, V.N.      702—704
Berg, I.David      702
Berger, Marcel, XI      2 11 20 21 23 26 28—31 33 38 42 59 67 70 76 77 79 92 109—111 139 145 148 150 151 158 162 163 168 169 172 173 187 188 196 206 311 315 327 329 349 353 355 358 365 372 375 380 385 388 399 415 420 426 460 556 568 572 581 586 604 670 679 693 713 717 739 757
Berger, Melvyn S.      493
Bergeron, Nicolas      636
Berndt, Jurgen      235 314
Bernoulli shift      498 515
Bertrand — Puiseaux formula      124 225
Besicovitch, A.S.      359 360 376 377 440
Besicovitch’s $1^{st}$ theorem      359 377
Besicovitch’s $2^{nd}$ theorem      377
Besse, Arthur L.      49 53 173 209 213 227 229 230 259 260 304 310 337 371 386 387 415 460 504 517 523 529 537 548 550—552 555 558 559 561 595 630 664 680 681 694 699 709 735 745—747
Bessel function      89
Bessieres, Laurent      548
Besson, Gerard      111 314 318 321 343 344 410 425 426 435 445 446 510 511 524 548 558 559 693 708 710
Betline, Nicole      399 420 422 689 694 696—700 743 744
Bets, Lipman      435
Betti number      177
Bianchi identity first      223 573 726
Bianchi identity second      731
Bicharacteristic      431
Bieberbach theorem      316 596
Billiard      4—9
Billiard table      4
biology      711
Biquard, Olivier      680
Biregular curve      12
Birkhoff canonical form      431
Birkhoff, G.D.      6 474
Bisectional curvature      682
Bishop theorem      334
Bishop, Richard L.      162 332 334 702
Bismut, Jean-Michel      700
Blair, David E.      529 682 684
Blaschke manifold      53 310 381
Blaschke, Wilhelm      53 153 463 521
Blatter, Christian      353 355
Bleecker, David      149
Bliss, Gilbert Ames      42
Bloch, C.      90 104 429 431
BM measure      508
Bochnak, Jacek      179
Bochner technique      621 631 733
Bochner — Weitzenboeck formula      289
Bochner, Salomon      399 428 604 616 621 622 682 732—734
Boeckx, Eric      236
Bogomolov, Fedor A.      714
Bokan, Neda      557
Bolsinov, Alexey V.      515
Bolyai, Johannes      115 194
Bombieri, Enrico      493
Bonnet theorem      140
Bonnet — Schoenberg — Myers theorem      266 290
Boothby, William M.      120 162
Borel, Armand      317 320 321 664 667 671
Born, Max      520
Bott, Raoul      178 452 478 489 518 699
Botvinnik, Boris      628
Boucetta, Mohamed      506
Boucksom, Sebastien      681
Bouncing, mirror      4
Boundary      702
Bourbaki, Nicolas      710
Bourdon, Marc      702 706
Bourguignon, Jean-Pierre      97 434 436 551 555 562 606 607 622 681 684 696 698 710 735 742 743 762
Bowditch, Brian H.      253
Bowen — Margulis measure      508 509
Bowen, Rufus      508
Boy, Werner      28 153
Boyer, Charles P.      553 621 678 679
Brascamp, Herin Jan      92
Braunmuhl, A.      44
Bridson, Martin A.      706
Brin, Michael      703
Brocks, Reinhard      290
Bronshtein, I.U.      498
Brooks, Robert      444
Brown, Robert B.      671
Brownian motion      426 711
Bruning, Jochen      438
Brunn — Minkowski theorem      31
Bryant, Robert L.      672 707 709
BShm, Christoph      556 557
Buchdal, N.      684
Buchner — Wall theorem      308
Buchner, Michael A.      303 308
Bujalance, Emilio      317
Bumpy metric      491
Bundle fiber      118
Bundle unit tangent      383
Bunimovitch stadium      7
Bunimovitch, Leonid A.      7 460
Bunke, Ulrich      416 420 450 453
Burago — Ivanov theorem      525
Burago, D.      343 525
Burago, Yu.D.      4 29 31 198 328 618 704
Burger, M.      681 701
Burns, Keith      483 484 512 515
Burstall, F.E.      228
Busemann function      289 505 612 613 622
Busemann, Herbert      623 705 708
Buser, Peter      99 107 196 201 256 257 316 348 359 366 399 416 434 446—449 460 471 596 637 640
Calabi, Eugenio      26 256 286 353 359 360 371 399 476 555 620 623 680 682 691 699
Calculus of variations      17
Calibration      511 693
Camera      3
Canonical Laplacian      693
Canonical transformation      427
Cao, Jian Guo      347 476 688
Caratheodory, Constantin      54 706
Caratheodory’s conjecture      54
Carnot — Caratheodory metric      309 636 706
Carnot, Sadi      706
Cartan surface theorem      234
Cartan — Janet theorem      238
Cartan, Elie      162 172 209 212 228 234 235 255 272 276—280 282 303 313 321 399 414 420 541 664 695 696 716 766
Catanese, Fabrizio      560
Category of a compact manifold      390
Catenoid      70
Cauchy’s polyhedron theorem      148
Caustic      7 107
Cayley numbers      170 172
Cayley plane      172 593
Center of mass      255—257 279 511 644
Characteristic class      740
Characteristic number      742 743
Characteristic secondary      453 697
Chart      33 162
Chavel, Isaac      88 92 101 110 111 134 153 162 269 296 302 327 328 332 349 350 377 387 399 420
Chazarain, J.      429
Cheeger finitehess theorem      469 642
Cheeger — Colding theorem      624
Cheeger — Rong theorem      542
Cheeger, Jeff      134 209 251 252 257 280 286 289 294 296—302 339 347 348 420 434 454 469 540 542 544 547 574 578 92 595 601 602 606 607 609 611 614 622 624 626 641—644 650 652 656—660 686 688 698 703—705
Cheeger’s constant      339
Chen, Bang-Yen      716
Chen, Bing-Long      595
Chen, Haiwen      573 617
Chen, Jingyi      70
Cheng, Shiu Yuen      268 269 289 411 433
Chern class      740
Chern, Shiing-Shen      67 123 153 399 607 697 736 737 740 743
Chernov, N.I.      7
Chevalley, Claude      399 696
Chinburg, Ted      474
Chmutov, S.      29
Cho, Yunhi      202
Chopp, David L.      70
Chopping      688
Choquet, Gustave      350 469
Chow, Bennett      277 444 503 554
Christodoulou, Demetrios      710
Chromatic number      435 439
Churchill, R.V.      227
Circle problem      89 412
Classical mechanics      219—220
Clifford algebra      694
Closed differential form      185
co-closed      see “Differential form”
Codazzi — Mainardi equations      232 716
Cohn-Vossen, Stefan      120 145 687
Cohomology      177
Colding $L^1$ theorem      286
Colding $L^2$ theorem      288
Colding, Tobias H.      286 288 601—603 624 626 656 660 686 688 705
Colin de Verdiere, Yves      105 110 157 429 430 432 437 439 440
Collapsing      542
Collar      636
Complete metric space      249
Complete of holonomy      666
Complex isotropic plane      574
Complex sectional curvature      573
Computable function      563
Computer programming      2
Concavity      12
Concentration phenomenon      329 714
Condition C of Palais — Smale      550 551 557 605
Conductivity      83
Cone metric      686
Cone topology      635
Cone volume      686
Configuration space      507
conformal      177 198
Conformal representation theorem      277
Conformally flat      228
Conical singularity      703
Conjecture Alexandrov’s      65
Conjecture Caratheodory      54
Conjecture Willmore      152
Conjugate geodesic flows      522
Conjugate locus      144
Conjugate point      144 292
Connected sum      218
Connection      724
Connection Levi-Civita      723 725
Connection linear      724
Connelly, R.      148
Connes, Alain      551 697 709 711
Contact geometry      684
Contractibility function      392 648 649
Contractible      469
Contractible geometrically      392
Contractible locally geometrically      392
Contraction of indices      722
Control theory      19
Controlled topology      599 649
Convex polygon      6
Convexity      4 251—253
Convexity radius      302 292—310
Convolution      420
Conway, John H.      99 110 365 441 609 610
Coordinate system      162
Coordinates harmonic      245 291 651 655
Coordinates normal      221
Corlette, Kevin      320 597 681 701
Cornfeld, I.P.      460
Coste, Michel      179
1 2 3 4 5 6 7
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