Riemannian Geometry

Capa
Walter de Gruyter, 3 de mai. de 2011 - 419 páginas

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Please submit any book proposals to Niels Jacob.

Titles in planning include

Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018)
Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019)
Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019)
Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press)
Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021)
Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

 

Conteúdo

Foundations
1
11 Differentiable Manifolds
8
12 Tensor Bundles
13
13 Immersions and Submersions
23
14 Vector Fields and Tensor Fields
31
15 Covariant Derivation
39
16 The Exponential Mapping
53
17 Lie Groups
59
25 Appendix The S1 and the Z2action on AM
196
26 Index and Curvature
203
26 Appendix The Injectivity Radius for 14pinched Manifolds
212
27 Comparison Theorems for Triangles
215
28 The Sphere Theorem
229
29 Noncompact Manifolds of Positive Curvature
240
Structure of the Geodesic Flow
256
32 Properties of the Geodesic Flow
265

18 Riemannian Manifolds
67
19 Geodesics and Convex Neighborhoods
78
110 Isometric Immersions
86
111 Riemannian Curvature
97
112 Jacobi Fields
109
Curvature and Topology
124
21 Appendix Orientation
136
22 Symmetric Spaces
141
23 The Hilbert Manifold of H1curves
158
24 The Loop Space and the Space of Closed Curves
170
25 The Second Order Neighborhood of a Critical Point
181
33 Stable and Unstable Motions
279
34 Geodesics on Surfaces
288
35 Geodesics on the Ellipsoid
303
36 Closed Geodesies on Spheres
324
37 The Theorem of the Three Closed Geodesics
337
38 Manifolds of NonPositive Curvature
350
39 The Geodesic Flow on Manifolds of Negative Curvature
363
310 The Main Theorem for Surfaces of Genus 0
380
References
393
Index
403
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