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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2 ページ
... exist one important example of an n-dimensional vector space over R which has a distinguished or canonical basis—a basis which is somehow given by the nature of the space itself. We refer to the vector space of n-tuples of real numbers ...
... exist one important example of an n-dimensional vector space over R which has a distinguished or canonical basis—a basis which is somehow given by the nature of the space itself. We refer to the vector space of n-tuples of real numbers ...
3 ページ
... exists an isometry, that is, an isomorphism preserving the inner product, of W onto R" interpreted as Euclidean vector space. 4. Show that C", the space of n-tuples of complex numbers, may be placed in one-to-one correspondence with R ...
... exists an isometry, that is, an isomorphism preserving the inner product, of W onto R" interpreted as Euclidean vector space. 4. Show that C", the space of n-tuples of complex numbers, may be placed in one-to-one correspondence with R ...
11 ページ
... exists a continuous curve f(s), 0 < s > 1, with f(0) = p, f(1) = q. 4. Show that the (connected) components of a manifold M are open sets and are countable in number. 4 Further Examples of Manifolds. Cutting and Pasting A hemispherical ...
... exists a continuous curve f(s), 0 < s > 1, with f(0) = p, f(1) = q. 4. Show that the (connected) components of a manifold M are open sets and are countable in number. 4 Further Examples of Manifolds. Cutting and Pasting A hemispherical ...
16 ページ
... exist corresponding bases of both planes p and q (considered as r-dimensional subspaces of R", as a vector space) such that corresponding basis vectors are close, say, for example, that their differences have norm less than some e > 0 ...
... exist corresponding bases of both planes p and q (considered as r-dimensional subspaces of R", as a vector space) such that corresponding basis vectors are close, say, for example, that their differences have norm less than some e > 0 ...
21 ページ
... exists at each point of U for 1 < j < n, this defines n functions on U. Should these functions be continuous on U ... exist constants b1, ..., b, and a function r(x, a) defined on a neighborhood V of a e U which satisfy the following two ...
... exists at each point of U for 1 < j < n, this defines n functions on U. Should these functions be continuous on U ... exist constants b1, ..., b, and a function r(x, a) defined on a neighborhood V of a e U which satisfy the following two ...
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