Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Gallot S., Hulin D. — Riemannian Geometry
Gallot S., Hulin D. — Riemannian Geometry

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Riemannian Geometry

Авторы: Gallot S., Hulin D.

Аннотация:

This book is intended for a one year course in Riemannian Geometry. It will serve as a single source, introducing students to the important techniques and theorems while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian Geometry. Instead of variational techniques, the author uses a unique approach emphasizing distance functions and special coordinate systems. He also uses standard calculus with some techniques from differential equations, instead of variational calculus, thereby providing a more elementary route for students. Many of the chapters contain material typically found in specialized texts and never before published together in one source. Key sections include noteworthy coverage of: geodesic geometry, Bochner technique, symmetric spaces, holonomy, comparison theory for both Ricci and sectional curvature, and convergence theory. This volume is one of the few published works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory as well as presenting the most up-to-date research including sections on convergence and compactness of families of manifolds. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help to motivate readers to deepen their understanding of the subject.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 248

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
(Almost) effective      2.36.
(Complex) projective space      1.10 1.19 1.96 2.29 2.36 2.45 2.110 2.114 3.58 3.66 4.35.
(Flat) tori      2.22 ff. 2.82 2.114 3.44 3.75 3.84 IV.E 4.35 4.37.
(Gaussian) curvature      5.3 ff.
(Infinitesimal) isometry (or Killing field)      2.62 4.40.
(Isotropy irreducible) homogeneous space      2.28 3.64 5.24.
(Local) flow      1.57 ff. 1.75
(Local) one-parameter subgroup      1.59 ff. 1.76.
(Local) trivialisations      1.32 1.91 4.26.
(Negative) curvature      3.87 3.89 3.110.
(Normal) homogeneous space      3.63 3.64.
(Principal) curvatures      5.6 5.7 5.9.
(Real) projective space      1.10 1.13 1.89 1.101 2.45 2.46 2.82 2.108 2.114. 3.49 3.74 3.83 5.25.
(Ricci) curvature      3.18 3.21 3.22 3.85 3.100 3.116 3.127 3.128 4.36 4.40 4.67
(Riemannian) covering map      2.17 ff. 2.106 3.13 4.17.
(Riemannian) submanifold      2.14 2.56 2.77 V.A.
(Riemannian) submersion      2.27 ff. 2.109 3.61
(Scalar) curvature      3.19 3.22 3.97 3.127.
(Sectional) curvature      3.7. 3.8 3.17 3.35 3.65 3.68 III.F 3.87 3.110 3.112 3.115.
(Totally geodesic) submanifold      5.4.
(Totally) geodesic      5.2.
Abstract manifold      1.8.
Adjoint representation      1.80 2.41.
Antisymmetrisation      1.117.
Atlas      1.6 4.1.
Bianchi identity      3.5 3.8 3.119 3.134.
Bishop — Gromov inequality      3.101 3.106 4.19 4.68
Boundary      4.2 4.71.
Bracket      1.52 1.66 1.71 1.112 2.49 3.4 3.56.
Bundle      1.32 1.91 1.103
Catenoid      2.12.
Christoffel symbols      2.54 2.100.
Cohomology      4.22 4.34 4.37.
complete      2.101 ff. 2.109 2.111 3.87 5.4.
Conformally flat      3.130 ff.
Connection      2.49 ff. 2.58 3.52
Convex submanifold      5.14 ff.
Convexity radius      2.90.
Covariant derivative      2.60.
Covariant derivative along a curve      2.68 ff.
Covering map      1.83 ff. 2.80.
Curvature      III V.A.
Derivation      1.45 ff. 3.4 4.36.
Diameter      3.85 4.39 4.69.
Diffeomorphism      1.18.
Differential form      I.G IV.B IV.C.
Differential operator      4.24 ff.
Dirichlet problem      IV.D. 4.68.
Distance      2.91 4.16 4.17.
Divergence      3.125 4.4bis 4.8.
Effective      2.36.
Embedding      1.18 ff. 1.133 5.6.
Energy      2.96 ff. III.E IV.D.
Exponential map (Lie groups)      1.76 ff. 2.87 2.90.
Exponential map (Riemannian Geometry)      2.86 ff. 2.90 3.46 3.87.
Flat      3.82 4.26.
Free action      1.86 ff.
Gauss equation (theorema egregium)      5.5 5.8.
Gauss lemma      2.93 3.70.
Gauss map      5.16.
Gauss — Bonnet theorem      3.111.
Gauss — Codazzi equation      5.8.
Geodesic      2.77 ff. 2.94 2.109 3.45 5.4.
Germ      1.44.
Haar measure      1.129 ff.
Hadamard theorem      5.16.
Hadamard — Cartan theorem      3.87.
Harmonic forms      4.32bis ff.
Heintze — Karcher inequality      4.21 4.71.
Heisenberg group      2.90 3.100.
Helicoid      2.12 5.11.
hessian      2.64 3.37 4.15 4.16.
Hodge laplacian      4.29.
Hodge — de Rham theorem      4.34 4.37.
Homogeneous space      1.97 2.33 2.108 3.21 3.64 3.65.
Homotopy      3.35 3.36 3.89 III.I 4.38.
Hopf conjecture      3.16.
Hopf Rinow theorem      2.103.
Horizontal      2.26 2.109 3.52
Hyperbolic space      2.10 2.11 2.65 2.80 2.83 3.14 3.48 3.51 3.82.
Hyperboloid      5.11.
Immersion      1.15 ff. 5.10.
Interior product      1.105 1.121 4.6.
Isometry      2 5 2.12 2.20 2.28 2.34 2.106.
Isoperimetric (inequality)      4.71.
Isotropy group      1.99 ff.
Isotropy representation      2.39 ff.
Jacobi fields      III.C III.E III.F III.G III.H.
Jacobi identity      1.53 1.71 1.112 3.5 3.134.
Killing form      2.48.
Klein bottle      1.89 2.25 2.82 2.83 4.47.
Length      2.6 2.14 2.91 3.31 3.34.
Lens space      3.83.
Levi-Civita connexion      2.51.
Lie algebra      1.71.
Lie derivative      1.109 ff. 1.115 1.121 2.61 3.4.
Lie group      1.70 ff. 1.129 2.34 2.47 2.108 3.17 3.81 3.84 3.84 3.86 3.105.
Local operator      1.111 1.113 4.27.
Mean curvature      4.21 V.C.
Minimal (geodesic)      2.95 2.103 2.111 3.89.
Minimal surface, minimal submanifold      V.C.
Moebius band      1.11 1.13 1.35.
Musical isomorphisms      2.66.
Neumann problem      4.41 4.68.
Normal coordinates      2.100.
Orientation      1.12 1.13 1.31 1.127 3.35 IV.A. .5.16.
Orientation atlas      1.12.
Parallel, parallel transport      2.71 ff. 2.83 3.35 3.57.
Partition of unit      1.128 I.H 2.2 3.91.
Periodic geodesies      2.91.
Polar coordinates      2.4 2.92 3.50.
Product manifold      1.13 2.27.
Product metric      2.15 2.27 3.15.
Proper action      1.85 ff.
Pseudo-sphere      2.13.
Pull-back      1.106 ff. 1.120
Second fondamental form      4.21 ff. 5.20.
Section      1.34 ff.
Shape operator      5.2.
Sphere      1.2 1.10 1.19 1.38 1.93 1.101 1.118 2.32 2.40 2.45 2.57 2.62 2.64 2.70 2.80 2.114 3.14 3.47 3.97 4.48 5.24.
Stenographic chart      1.10 1.28 1.39.
Submanifold      1.1 ff. 1.9 1.19 1.133 2.8.
Submersion      1.13 ff. 1.90 5.12.
Tangent bundle      1.29 ff. 1.40
Tangent vector      1.21 ff. 1.49.
Test function      1.51.
Torsion      2.50.
Torus      1.2 1.4 1.10 1.39 1.89 2.57.
Transitions functions      1.6.
Transitive action      1.100 ff.
Variation of a submanifold      5.18.
Whitney theorem      1.133.
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте