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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ix ページ
... 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 of a Surface 374 The ...
... 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 of a Surface 374 The ...
xiv ページ
... 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 every stage results that illustrate the power of these ...
... 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 every stage results that illustrate the power of these ...
41 ページ
... symmetric. As the following example shows, the differentiability of FT' is not a consequence of that of F, even when F is a homeomorphism. Let U = R and V = R and F: t H. s = to; this is a homeomorphism and F is analytic but FT': s - t ...
... symmetric. As the following example shows, the differentiability of FT' is not a consequence of that of F, even when F is a homeomorphism. Let U = R and V = R and F: t H. s = to; this is a homeomorphism and F is analytic but FT': s - t ...
42 ページ
... symmetry and reflexivity are part of the definition. (6.3) Lemma Let U, V, W be open subsets of R", F: U → V, G: V → W mappings onto, and H = Go F: U → W their composition. If any two of these maps is a diffeomorphism, then the third ...
... symmetry and reflexivity are part of the definition. (6.3) Lemma Let U, V, W be open subsets of R", F: U → V, G: V → W mappings onto, and H = Go F: U → W their composition. If any two of these maps is a diffeomorphism, then the third ...
67 ページ
... reflexivity and symmetry are obvious from the definition. It is important that F *, as well as F, be C* as the following example shows. (3.7) Example Let F: R → R be defined by 3 D | FF ER ENTIA B L E FUNCTIONS AND MAP PIN GS 67.
... reflexivity and symmetry are obvious from the definition. It is important that F *, as well as F, be C* as the following example shows. (3.7) Example Let F: R → R be defined by 3 D | FF ER ENTIA B L E FUNCTIONS AND MAP PIN GS 67.
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