An Introduction to Differentiable Manifolds and Riemannian GeometryAcademic Press, 1986/04/21 - 429 ページ An Introduction to Differentiable Manifolds and Riemannian Geometry |
この書籍内から
検索結果1-5 / 52
vii ページ
... Groups 81 The Action of a Lie Group on a Manifold. Transformation Groups 89 The Action of a Discrete Group on a Manifold 96 Covering Manifolds 101 Notes 104 1. Integration in R*. Domains of Integration 230 Basic Properties vii Contents.
... Groups 81 The Action of a Lie Group on a Manifold. Transformation Groups 89 The Action of a Discrete Group on a Manifold 96 Covering Manifolds 101 Notes 104 1. Integration in R*. Domains of Integration 230 Basic Properties vii Contents.
ix ページ
... Covering Spaces and the Fundamental Group 289 Notes 296 VII. Differentiation on Riemannian Manifolds 1. Differentiation of Vector Fields along Curves in R* 298 The Geometry of Space Curves 301 Curvature of Plane Curves 305 2 ...
... Covering Spaces and the Fundamental Group 289 Notes 296 VII. Differentiation on Riemannian Manifolds 1. Differentiation of Vector Fields along Curves in R* 298 The Geometry of Space Curves 301 Curvature of Plane Curves 305 2 ...
xv ページ
... covering spaces, discontinuous group action, and the fundamental group given earlier in the book. This book, as do many of the books in this subject, owes much to the influence of S. S. Chern. For many years his University of Chicago ...
... covering spaces, discontinuous group action, and the fundamental group given earlier in the book. This book, as do many of the books in this subject, owes much to the influence of S. S. Chern. For many years his University of Chicago ...
11 ページ
... covering (U.} of M by open sets has a locally finite refinement; more precisely, there is a covering (V, which (i) refines (U.} in the sense that each V, c U, for some o, and which (ii) is locally finite, that is, each pe M has a ...
... covering (U.} of M by open sets has a locally finite refinement; more precisely, there is a covering (V, which (i) refines (U.} in the sense that each V, c U, for some o, and which (ii) is locally finite, that is, each pe M has a ...
51 ページ
... covering by compatible coordinate neighborhoods, that is, a covering such that a change of local coordinates is given by C* mappings in R". Several examples are worked out in detail, the most complicated being the Grassmann manifold of ...
... covering by compatible coordinate neighborhoods, that is, a covering such that a change of local coordinates is given by C* mappings in R". Several examples are worked out in detail, the most complicated being the Grassmann manifold of ...
目次
1 | |
20 | |
51 | |
Chapter IV Vector Fields on a Manifold | 106 |
Chapter V Tensors and Tensor Fields on Manifolds | 176 |
Chapter VI Integration on Manifolds | 229 |
Chapter VII Differentiation on Riemannian Manifolds | 297 |
Chapter VIII Curvature | 365 |
References | 417 |
Index | 423 |
多く使われている語句
algebra basis bi-invariant C*-vector field compact completes the proof components connected coordinate frames coordinate neighborhood Corollary corresponding countable covariant tensor covering curve p(t defined definition denote derivative diffeomorphism differentiable manifold dimension domain of integration element equations equivalent Euclidean space example Exercise exists fact finite fixed point formula functions geodesic geometry given Gl(n hence homeomorphism homotopy identity imbedding inner product integral curve isometry isomorphism Lemma Let F Lie group G linear map mapping F matrix notation obtain one-parameter subgroup one-to-one open set open subset oriented orthogonal orthonormal parameter plane properly discontinuously properties prove rank real numbers regular submanifold Remark Riemannian manifold Riemannian metric Section Show structure submanifold subspace suppose surface symmetric tangent space tangent vector tensor field Theorem Let topology uniquely determined vector field vector space zero