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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... mapping from V" to V" (with elements written as n x 1 and m × 1 matrices), which is defined by y = Ax, is continuous. Identify the images of the canonical basis of V" as linear ... map X → AX, where A is a fixed m × m matrix and X is an ...
... mapping from V" to V" (with elements written as n x 1 and m × 1 matrices), which is defined by y = Ax, is continuous. Identify the images of the canonical basis of V" as linear ... map X → AX, where A is a fixed m × m matrix and X is an ...
33 ページ
... mappings of C*(a) to R with these properties; we may call the elements of Ø(a) “derivations” on C*(a) into R. We see ... map y1): C*(a) → R is linear. That yD satisfies the Leibniz rule for differentiation of products is equally easy ...
... mappings of C*(a) to R with these properties; we may call the elements of Ø(a) “derivations” on C*(a) into R. We see ... map y1): C*(a) → R is linear. That yD satisfies the Leibniz rule for differentiation of products is equally easy ...
34 ページ
... mapping is linear. If Z, - XX, + BY, e T.(R"), then for the directional derivatives we have for any fe C*(a), Z; fe &(X, f) + B(Y: f). If interpreted in terms of the operations in Ø(a), this means exactly that the mapping T.(R") → Z (a) ...
... mapping is linear. If Z, - XX, + BY, e T.(R"), then for the directional derivatives we have for any fe C*(a), Z; fe &(X, f) + B(Y: f). If interpreted in terms of the operations in Ø(a), this means exactly that the mapping T.(R") → Z (a) ...
35 ページ
... map X. — X: of T.(R") to Ø(a) is an isomorphism onto. Let h'(x", ..., x") = x'. Then denote by & the value of Dh ... linear operators on functions of C*(a) into R which satisfy the product rule of Leibniz, that is, the “derivations into ...
... map X. — X: of T.(R") to Ø(a) is an isomorphism onto. Let h'(x", ..., x") = x'. Then denote by & the value of Dh ... linear operators on functions of C*(a) into R which satisfy the product rule of Leibniz, that is, the “derivations into ...
39 ページ
... maps Co(U) into itself, a slight variation from the previous case. (This, in fact, is the customary use of the term “derivation” of an algebra. If A is an algebra over R, then a derivation is a map D: A → A which is linear and ...
... maps Co(U) into itself, a slight variation from the previous case. (This, in fact, is the customary use of the term “derivation” of an algebra. If A is an algebra over R, then a derivation is a map D: A → A which is linear and ...
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