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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viii ページ
... Algebra of Vector Fields on a Manifold 151 Frobenius' Theorem 158 Homogeneous Spaces 165 Appendix Partial Proof of Theorem 4.1 172 Notes 174 V. Tensors and Tensor Fields on Manifolds 1. Tangent Covectors 177 Covectors on Manifolds 178 ...
... Algebra of Vector Fields on a Manifold 151 Frobenius' Theorem 158 Homogeneous Spaces 165 Appendix Partial Proof of Theorem 4.1 172 Notes 174 V. Tensors and Tensor Fields on Manifolds 1. Tangent Covectors 177 Covectors on Manifolds 178 ...
xiii ページ
... algebra becomes lost—not irretrievably, but for all too long. Simple but nontrivial examples that illustrate the necessity for the high level of abstraction are not easy to present at this stage, and a realization of the power and ...
... algebra becomes lost—not irretrievably, but for all too long. Simple but nontrivial examples that illustrate the necessity for the high level of abstraction are not easy to present at this stage, and a realization of the power and ...
9 ページ
... algebraic topology. It was proved in 1911 by L. E. J. Brouwer and is known as Brouwer's theorem on invariance of domain. For a. (3.6) Theorem A topological manifold M is locally connected, locally compact, and a union of a countable ...
... algebraic topology. It was proved in 1911 by L. E. J. Brouwer and is known as Brouwer's theorem on invariance of domain. For a. (3.6) Theorem A topological manifold M is locally connected, locally compact, and a union of a countable ...
18 ページ
... algebraic equations, for example, So = {(x, y, z)|x* + y”-- z* = 1}. Show that the torus To may be given as the locus of an equation in x, y, z. seen that there are such alterations. For example, we may. Notes Curves and surfaces in ...
... algebraic equations, for example, So = {(x, y, z)|x* + y”-- z* = 1}. Show that the torus To may be given as the locus of an equation in x, y, z. seen that there are such alterations. For example, we may. Notes Curves and surfaces in ...
19 ページ
... algebraic topology, algebraic geometry, and elsewhere. The reader will find historical sketches in many of the references. In particular, Gauss's famous paper [1] is available in an annotated English translation and Riemann's Inaugural ...
... algebraic topology, algebraic geometry, and elsewhere. The reader will find historical sketches in many of the references. In particular, Gauss's famous paper [1] is available in an annotated English translation and Riemann's Inaugural ...
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