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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51 ページ
... submanifold and regular submanifold (Section 5). We require the latter to be subspaces and to be defined locally by the vanishing of some of the coordinates of suitable local coordinates in the ambient space. In Section 6 the concept of ...
... submanifold and regular submanifold (Section 5). We require the latter to be subspaces and to be defined locally by the vanishing of some of the coordinates of suitable local coordinates in the ambient space. In Section 6 the concept of ...
56 ページ
... submanifolds) An open subset U of a C* manifold M is itself a C* manifold with differentiable structure consisting of the ... submanifold of M. A particular case of some interest is the following. We consider the subset U = Gl(n, R) of M ...
... submanifolds) An open subset U of a C* manifold M is itself a C* manifold with differentiable structure consisting of the ... submanifold of M. A particular case of some interest is the following. We consider the subset U = Gl(n, R) of M ...
57 ページ
... submanifold of 4,0R). (1.7) Theorem Let M and N be C* manifolds of dimensions m and n. Then M × N is a C* manifold of dimension m + n with C* structure determined by coordinate neighborhoods of the form {U × V, p. x s), where U, q, and ...
... submanifold of 4,0R). (1.7) Theorem Let M and N be C* manifolds of dimensions m and n. Then M × N is a C* manifold of dimension m + n with C* structure determined by coordinate neighborhoods of the form {U × V, p. x s), where U, q, and ...
58 ページ
... submanifolds (to be defined). A two-dimensional submanifold of E° or R* is often called a surface and. 58 III Di FF ER ENTIA B L E M A N IF O L D S A N D S U B M A N | F O L DS.
... submanifolds (to be defined). A two-dimensional submanifold of E° or R* is often called a surface and. 58 III Di FF ER ENTIA B L E M A N IF O L D S A N D S U B M A N | F O L DS.
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