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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viii ページ
... Manifold 107 Vector Fields 116 One-Parameter and Local One-Parameter Groups Acting on a Manifold 123 The Existence ... Riemannian Metric 183 3. Riemannian Manifolds as Metric Spaces 187 4. Partitions of Unity 193 Some Applications of the ...
... Manifold 107 Vector Fields 116 One-Parameter and Local One-Parameter Groups Acting on a Manifold 123 The Existence ... Riemannian Metric 183 3. Riemannian Manifolds as Metric Spaces 187 4. Partitions of Unity 193 Some Applications of the ...
ix ページ
... Riemannian 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 ...
... Riemannian 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 ...
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 ...
xv ページ
... manifolds in Chapter VI. Numerous applications are given. It would be possible to use Chapters II-VI as the basis of a one-semester course for students who wish to learn the fundamentals of differentiable manifolds without any Riemannian ...
... manifolds in Chapter VI. Numerous applications are given. It would be possible to use Chapters II-VI as the basis of a one-semester course for students who wish to learn the fundamentals of differentiable manifolds without any Riemannian ...
12 ページ
... manifolds, can be formed by fastening together manifolds with boundary along their boundaries, that is, by identifying ... manifold M whose boundary 6M is the disjoint union of two circles, and (2) paste on a cylinder or “handle” so that ...
... manifolds, can be formed by fastening together manifolds with boundary along their boundaries, that is, by identifying ... manifold M whose boundary 6M is the disjoint union of two circles, and (2) paste on a cylinder or “handle” so that ...
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