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
... Tangent Vectors at a Point of R" 29 Another Definition of T.(R") 32 Vector Fields on Open Subsets of R" 37 The Inverse Function Theorem 41 The Rank of a Mapping 46 IV. Vector Fields on a Manifold The Tangent Space at. III. Notes 50 ...
... Tangent Vectors at a Point of R" 29 Another Definition of T.(R") 32 Vector Fields on Open Subsets of R" 37 The Inverse Function Theorem 41 The Rank of a Mapping 46 IV. Vector Fields on a Manifold The Tangent Space at. III. Notes 50 ...
viii ページ
IV. Vector Fields on a Manifold The Tangent Space at a Point of a Manifold 107 Vector Fields 116 One-Parameter and Local One-Parameter Groups Acting on a Manifold 123 The Existence Theorem for Ordinary Differential Equations 131 Some ...
IV. Vector Fields on a Manifold The Tangent Space at a Point of a Manifold 107 Vector Fields 116 One-Parameter and Local One-Parameter Groups Acting on a Manifold 123 The Existence Theorem for Ordinary Differential Equations 131 Some ...
ix ページ
... Vector Fields on Submanifolds of R" 307 Formulas for Covariant Derivatives 312 Vy, Y and Differentiation of Vector ... Tangent Bundle and Exponential Mapping. Normal Coordinates 335 Some Further Properties of Geodesics 342 Symmetric ...
... Vector Fields on Submanifolds of R" 307 Formulas for Covariant Derivatives 312 Vy, Y and Differentiation of Vector ... Tangent Bundle and Exponential Mapping. Normal Coordinates 335 Some Further Properties of Geodesics 342 Symmetric ...
xiv ページ
... vector bundles (more specifically to the tangent bundle). Thus it is not claimed that this is a comprehensive book; the student will emerge with gaps in his knowledge of various subjects treated (for example, Lie groups or Riemannian ...
... vector bundles (more specifically to the tangent bundle). Thus it is not claimed that this is a comprehensive book; the student will emerge with gaps in his knowledge of various subjects treated (for example, Lie groups or Riemannian ...
7 ページ
... tangent plane and a unit normal vector N,. There will be a coordinate axis which is not perpendicular to N, and some neighborhood U of p on So will then project in a continuous and one-to-one fashion onto an open set U" of the ...
... tangent plane and a unit normal vector N,. There will be a coordinate axis which is not perpendicular to N, and some neighborhood U of p on So will then project in a continuous and one-to-one fashion onto an open set U" of the ...
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