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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... isomorphic. It is important to note that this isomorphism depends on choices of bases in the two spaces; there is in general no natural or canonical isomorphism independent of these choices. However, there does exist one important ...
... isomorphic. It is important to note that this isomorphism depends on choices of bases in the two spaces; there is in general no natural or canonical isomorphism independent of these choices. However, there does exist one important ...
3 ページ
... isomorphism? 5. Exhibit an isomorphism between the vector space of m x n matrices over R and the vector space R”. Show that the map X → AX, where A is a fixed m × m matrix and X is an arbitrary m x n matrix (over R), is continuous in ...
... isomorphism? 5. Exhibit an isomorphism between the vector space of m x n matrices over R and the vector space R”. Show that the map X → AX, where A is a fixed m × m matrix and X is an arbitrary m x n matrix (over R), is continuous in ...
29 ページ
... isomorphic, that is, there is an isomorphism determined in some unique fashion by the geometry of the space—not chosen by us. (Without the restriction of naturality, the statement would be trivial since any two vector spaces of the same ...
... isomorphic, that is, there is an isomorphism determined in some unique fashion by the geometry of the space—not chosen by us. (Without the restriction of naturality, the statement would be trivial since any two vector spaces of the same ...
30 ページ
... isomorphism. This requires that X, + Y. = 0, "(p.(X.) + p.(Y.)). 3.x. = q', '(xq),(Xa)), o, e R, the right-hand side being used to define the operations on the left. Clearly we are being guided by the fact that R" and E" may be ...
... isomorphism. This requires that X, + Y. = 0, "(p.(X.) + p.(Y.)). 3.x. = q', '(xq),(Xa)), o, e R, the right-hand side being used to define the operations on the left. Clearly we are being guided by the fact that R" and E" may be ...
31 ページ
... isomorphisms of T.(E”) and T.(E*) given by the translations of E°. For example, there is no natural isomorphism of ... isomorphism—is not suitable for generalization in its present form. Therefore we shall give two further methods for ...
... isomorphisms of T.(E”) and T.(E*) given by the translations of E°. For example, there is no natural isomorphism of ... isomorphism—is not suitable for generalization in its present form. Therefore we shall give two further methods for ...
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