An Introduction to Differentiable Manifolds and Riemannian GeometryAcademic Press, 1986/04/21 - 429 ページ An Introduction to Differentiable Manifolds and Riemannian Geometry |
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vii ページ
... 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.
... 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.
viii ページ
... Properties of the Riemann Integral 231 2. A Generalization to Manifolds 236 Integration on Riemannian Manifolds 240 Integration on Lie Groups 244 Manifolds with Boundary 251 Stokes's Theorem sor Manifolds with Boundary 259 Homotopy of ...
... Properties of the Riemann Integral 231 2. A Generalization to Manifolds 236 Integration on Riemannian Manifolds 240 Integration on Lie Groups 244 Manifolds with Boundary 251 Stokes's Theorem sor Manifolds with Boundary 259 Homotopy of ...
ix ページ
... Properties of Geodesics 342 Symmetric Riemannian Manifolds 351 Some Examples 357 Notes 364 : VIII. Curvature 1. The Geometry of Surfaces in E° 366 The Principal Curvatures at a Point of a Surface 370 2. The Gaussian and Mean Curvatures ...
... Properties of Geodesics 342 Symmetric Riemannian Manifolds 351 Some Examples 357 Notes 364 : VIII. Curvature 1. The Geometry of Surfaces in E° 366 The Principal Curvatures at a Point of a Surface 370 2. The Gaussian and Mean Curvatures ...
xv ページ
... properties; a fairly extensive discussion of examples is included. Chapter IV is particularly concerned with vectors and vector fields and with a careful exposition of the existence theorem for solutions of systems of ordinary ...
... properties; a fairly extensive discussion of examples is included. Chapter IV is particularly concerned with vectors and vector fields and with a careful exposition of the existence theorem for solutions of systems of ordinary ...
3 ページ
... properties: (a) ||x + y | < |x| + |y|; (b) ||x|| – ||y|| < |x – y (c) |&x| = |x||x|, c e R; and (d) explain how (a) is related to the triangle inequality of d(x, y). * 7. Show that an isometry of a Euclidean vector space onto itself has ...
... properties: (a) ||x + y | < |x| + |y|; (b) ||x|| – ||y|| < |x – y (c) |&x| = |x||x|, c e R; and (d) explain how (a) is related to the triangle inequality of d(x, y). * 7. Show that an isometry of a Euclidean vector space onto itself has ...
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