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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11 ページ
... finite refinement; more precisely, there is a covering (V, which (i) refines (U.} in the sense that each V, c U, for some o, and which (ii) is locally finite, that is, each pe M has a neighborhood W which intersects only a finite number ...
... finite refinement; more precisely, there is a covering (V, which (i) refines (U.} in the sense that each V, c U, for some o, and which (ii) is locally finite, that is, each pe M has a neighborhood W which intersects only a finite number ...
40 ページ
... finite collection of n-balls in R" – F such that U*- B,2(a) = K. It is possible to find such a collection because of the compactness of K and since K C F = 2). For B.(a) let g(x) have the properties above and define a(x) by ce)-1-10-0 ...
... finite collection of n-balls in R" – F such that U*- B,2(a) = K. It is possible to find such a collection because of the compactness of K and since K C F = 2). For B.(a) let g(x) have the properties above and define a(x) by ce)-1-10-0 ...
56 ページ
... finite-dimensional vector space V over R can be identified with R", n = dim V, once a basis e1, ..., e, is chosen: w = x'el + · · · + x"e, is identified with (x', ..., x") in R"; similarly, the m x n matrices (a) with R" with the matrix ...
... finite-dimensional vector space V over R can be identified with R", n = dim V, once a basis e1, ..., e, is chosen: w = x'el + · · · + x"e, is identified with (x', ..., x") in R"; similarly, the m x n matrices (a) with R" with the matrix ...
96 ページ
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97 ページ
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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