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
... Manifold The Tangent Space at. III. Notes 50 Differentiable Manifolds and Submanifolds The Definition of a Differentiable Manifold 52 Further Examples 60 Differentiable Functions and Mappings 65 Rank of a Mapping. Immersions 69 ...
... Manifold The Tangent Space at. III. Notes 50 Differentiable Manifolds and Submanifolds The Definition of a Differentiable Manifold 52 Further Examples 60 Differentiable Functions and Mappings 65 Rank of a Mapping. Immersions 69 ...
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
... Manifolds 317 Constant Vector Fields and Parallel Displacement 323 4. Addenda to the Theory of Differentiation on a Manifold 325 The Curvature Tensor 325 The Riemannian Connection and Exterior Differential Forms 328 Geodesic Curves on ...
... Manifolds 317 Constant Vector Fields and Parallel Displacement 323 4. Addenda to the Theory of Differentiation on a Manifold 325 The Curvature Tensor 325 The Riemannian Connection and Exterior Differential Forms 328 Geodesic Curves on ...
xiii ページ
... differentiable manifolds has become useful—even mandatory—in an ever-increasing number of areas of mathematics and of its applications. This is not too surprising, since differentiable manifolds are the underlying, if unacknowledged ...
... differentiable manifolds has become useful—even mandatory—in an ever-increasing number of areas of mathematics and of its applications. This is not too surprising, since differentiable manifolds are the underlying, if unacknowledged ...
xiv ページ
... manifold theory: differential topology, Lie groups, symmetric and homogeneous spaces, harmonic analysis, dynamical systems, Morse theory, Riemann surfaces, and so on. Finally, it should be said that the author has tried to include at ...
... manifold theory: differential topology, Lie groups, symmetric and homogeneous spaces, harmonic analysis, dynamical systems, Morse theory, Riemann surfaces, and so on. Finally, it should be said that the author has tried to include at ...
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