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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
Cotangent bundle      183
Countable at infinity      163
Counting function      468 532
Courant, Richard      44 88 89 91 110 111
Courtois, Gilles      314 318 321 445 446 510 511 524 548 558 559 693 708 710
Covariant derivative      264 401 525 730
Covering normal      168
Covering space      167 203—206
Covering space Riemannian      203
Covering universal      168
Cox, David A.      680
Coxeter, H.S.MacDonald      2
Critical for the distance function      590
Critical lattice      365
Critical point      478
Crittenden, Richard J.      162
Croft, Hallard T.      13
Croke, Christopher B.      65 97 362 380 381 390 391 434 444 445 493 524 525 702 717
Croke’s embolic theorem      381
Cross ratio      197
Crushed ice      440
Cursed exotic $\mathbb {KP}^n$      520
Curvature      XI 723
Curvature algebraic      17
Curvature bisectional      682
Curvature complex sectional      573
Curvature Gaub      56
Curvature geodesic of curves on surfaces      39
Curvature holomorphic      682
Curvature mean      56
Curvature of hyperbolic space      198
Curvature of plane curves      13
Curvature of surfaces      222
Curvature operator      573 615
Curvature principal, of surface      53—61
Curvature radius of      13
Curvature ratio      594
Curvature Ricci      267
Curvature Ricci bounded      285—290
Curvature Ricci lower bounds      332—338
Curvature Riemann curvature tensor      117 220—224 726
Curvature sectional      224—227
Curvature sectional bounded      281—285
Curvature sectional constant      274—277 315—320
Curvature sectional nonpositive      277—280
Curvature sectional upper bounds      330—332
Curve biregular      12
Curve geometric      11
Curve heat shrinking      27 493
Curve parallel      13
Curve parameterized      11
Curve plane      9—31
Curve plane simple      12
Curve regular      11
Cut locus      44 139—145 302
Cut point      143 293
Cut value      75 293
Dai, Xianzhe      290 651
Dai-Wei theorem      290
Damek, Ewa      314
Damour, Thibault      167
Dancer, Andrew      553
Darboux, Gaston      234
de Kerekjarto, Bela      176
De Rham cohomology      186
de Rham reducibility theorem      251
de Rham theorem      177 178 186 188 248
de Rham, Georges      see “Rham Georges
Deck transformation      167
Degen, W.L.F.      305
Degree of a map      158
Delaunay surface      61
Deligne, Pierre      320 683
Derdzinski, Andrzej      551
Derivation      181
Derivative      182
Derivative covariant      730
Deschamps, Annie      520
Determinant of the Laplacian      443
deTurck, Dennis M.      550
di Meglio, J.-M.      26
di Scala, Antonio J.      234
Diameter      250
Diameter observable      713
Diastasis      555 682
Dierkes, Ulrich      69 70
Dieudonne, Jean      174 190 232 716 736
Diffeomorphism      163
Differential      182
Differential character      698
Differential complex      689
Differential form      184—190 689 721
Differential form closed      185
Differential form co-closed      691
Differential form exact      186
Differential form harmonic      691
Differential form intrinsically harmonic      691
Diffusion of cycles      358 546 598
Dirac $\delta$ function      418
Dirac operator      695
Dirac, Paul A.M.      695
Dirichlet principle      88 408 715
Dirichlet problem      85
Dirichlet quotient      88 394 408 459
do Carmo, Manfredo Perdiggo      2 19—21 42 59 67 70 73 120 134 151 152 162 252 269 280 293 296 300
Dobrushin, R.L.      460
Dodziuk, Jozef      434 435
Dombrowski, Peter      120 123 125 138 232
Donaldson, S.K.      179 528 558 698 701
Donati, Leonbattista      79
Donnay, Victor J.      515
Donnelly, Harold      438 453
Double soul problem      619
Doubling property      335
Doyle, Peter      99
Druet, Olivier      349
Drum      91
Dubrovin, B.A.      168
Duistermaat, J.J.      429 430
Durumeric, Oguz      586 593
Duzhin, S.      29
Dvoretzky, Aryeh      74 329
Dyck, Walther      153
Dynkin, E.B.      208 606 774
D’Ambra, Giuseppina      456 710
Easley, Kevin L.      710
Eberlein, Patrick      503 504 509 523 632 633 635 636 638 639 687 688
Ebin, David G.      134 209 251 252 280 294 296 300 302 562 578 644 710
Ecker, Klaus      70
Economics      219
Eells, Jr.James      61 151 701
Efficient ball packing      641
Egorov, Yuri V.      437
Ehresmann, Charles      680 724
Ehrlich, Paul E.      710
Eigenfunction of $\Delta$      85 404
Eigenvalue of $\Delta$      85 404
Eigenvalue small      447
Einstein metric      546 549
Einstein sign      549
Einstein, Albert      291 655 775
El-Alaoui, El-H.Ch.      309 707
Ellipsoid      43 144 257 293 305 464 515
Elliptic point of a surface      79
Elliptic rational homotopy      619
Elliptic rationally      619
Ellis, G.F.R.      710
Elworthy, David      426
Embedded submanifold      169
Embedding      59
Embedding isometric      237
Embolic constant      380 532
Embolic functional      532 563
END      613
Energy of a map      700
entropy      501—503
Entropy measure      502
Entropy metric      9 502
Entropy topological      9 501
Entropy volume      501
Epstein, D.B.A.      223 731
Equichordal problem      13
Erdos, P.      104 365 412
Ergodicity      7 9 26 437 499
Eschenburg, Jost-Hinrich      209 282 284 337 556 581 605 612
Escobar, J.      347
Essential      369
Estimate Weyl eigenvalue      421
Etayo, Jose J.      317
Euclid      115
Euclid fifth postulate      115
Euclidean geometry      2—114
Euclidean plane      2
Euler angles      116 164
Euler characteristic      55 154 155 157 177 354 423 452 735 741 742
Euler form      737
Euler theorem      308
Exact differential form      186
Excess of a triangle      286
Exotic $\mathbb {KP}^n$      520
Exotic $\mathbb {KP}^n$ cursed      520
Exotic quaternionic projective plane      490
Exotic sphere      178 582
Exponential map      184 244 271—274
Exterior algebra      184
Exterior calculus      184
Exterior derivative      185 689
Exterior product      185
F polarized      540 547 658
F pure polarized      540 658
F structure      540 542 547 658
Faber — Krahn theorem      94 426
Fabricius-Bjerre, Fr.      28
Falconer, Kenneth J.      13
Farber, Michael      691
Farrell, F.T.      318 523 596 597 637 687
Fdix, Yves      619
Federer, Herbert      717
Fefferman, Charles      438
Ferrand, Emmanuel      29
Ferrand, Jacqueline      268
Ferus, D.      228
Feshbach, Herman      44 89 91
Fet, A.I.      489
Feynman, Richard P.      11 428
Fiat      124 316
Fiat conformally      228
Fiat torus      204 466
Fiber bundle      118 697
Filling radius      367
Filling value      565
Filling volume      367
Finely corrugated wrinkling      149
First Bianchi identity      223 573 726
First fundamental form      117 232
First variation      4 337
Flaminio, Livio      511
Floer homology      551
Focal value      345
Focusing      7
Focusing automatic      3
Foliation Riemannian      709
Fomenko, A.T.      168
Foulon, Patrick      503 524 709 710
Fourier integral operator      427 437
Fourier series      30
Franks, John      494 495
Freed, Daniel S.      698
Freedman, Michael      372
Friedrich, Thomas      694
Frobenius theorem      720
Frohlich, Jurg      665 681
Fuchs, Dmitry      73
Fueter, Rudolf      680
Fukaya, Kenji      540 579 596 625 636 640 651 652 656—660
Fundamental domain      204
Fundamental solution heat equation      100 406 418
Fundamental tone      87 92
Funk, P.      462
Futaki, A.      555
Gaffney, Matthew P.      452
Gage, Michael      28 493
Galicki, Krzysztof      553 621 678 679 703
Gallot, Sylvestre F.L.      59 134 162 179 193 236 246 251 252 260 275 280 286 294 303 304 314 318 321 327 328 332 343 344 348 410 425 426 445 446 510 511 524 548 558 559 573 595 624 661 693 708 710
Gal’perin, G.A.      7 477
Gamboa, Jose M.      317
Gao, L.Zhiyong      595 656 661
Gaps spectral      417
Gardner, Richard J.      13
Gasqui, Jacques      522 557
Gaub — Bonnet theorem      125—130 547
Gaub — Bonnet theorem global      155
Gaub — Bonnet theorem local      125
Gauduchon, Paul      109 111 399 415 420 558 680 696
Gaufi circle problem      89 104 412
Gaufi curvature      56
Gaufi equation      132 232
Gaufi equations      716
Gaufi lemma      131
Gaug, Carl Friedrich      33 115 116 119—134 194
Gauld, David B.      176
Gaussian orthogonal ensemble      450
Gauthier, J.-P.      309 707
Gel’fand, I.M.      440 441 709
Generatrix      56 70
GENERIC      78
Genus      155 354
Geodesic closed      50 51
Geodesic flow      X 383 398 417 458—460 462 464 470 472 473 482 498
Geodesic loop      51
Geodesic minimal      244
Geodesic on surfaces      38—53
Geodesic primitive      470
Geodesic space      705
Geodesy      3
Geometric curve      11
Geometric hierarchy      311—321
Geometric measure theory      190 344 627 717
Geometric number theory      365
Geometrically contractible      392
Geometrically locally      392
Geometry Euclidean      2—114
Gerber, Marlies      512 515
Getzler, Ezra      399 420 422 689 694 696—700 743 744
Ghost geodesic      466
Gibbons, G.W.      621
Gil-Medrano, Olga      710
Gilkey, Peter B.      399 420 422 452 453 557 684 689 694 697—700 742—744
Gillet, Henri      698 700
Girard, Albert      38
Glide in hyperbolic plane      447
Gluck, Herman      24 144 308
Gluing      173—174 215—218 542
Gluing of hyperbolic surfaces      216
Godbillon, Claude      709
Golden ratio      258 466
Golden triangle      723
Goldschmidt, Hubert      522
Goncharov, Alexander      320
Gorbatsevich, V.V.      208
1 2 3 4 5 6 7
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