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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xiv ページ
... compact Lie groups is demonstrated and applied to prove the complete reducibility of their linear representations. Then, in a later chapter, compact groups are used as simple examples of symmetric spaces, and their corresponding ...
... compact Lie groups is demonstrated and applied to prove the complete reducibility of their linear representations. Then, in a later chapter, compact groups are used as simple examples of symmetric spaces, and their corresponding ...
xv ページ
... compact Lie groups and Riemannian manifolds of constant curvature are both discussed in some detail as examples of the general theory. This discussion is based on a fairly complete treatment of covering spaces, discontinuous group ...
... compact Lie groups and Riemannian manifolds of constant curvature are both discussed in some detail as examples of the general theory. This discussion is based on a fairly complete treatment of covering spaces, discontinuous group ...
7 ページ
... compact while the other is not. (3.4) Example Our final example is that of the surface of revolution obtained by revolving a circle around an axis which does not intersect it. The figure we obtain is the torus or “inner tube” (denoted T ...
... compact while the other is not. (3.4) Example Our final example is that of the surface of revolution obtained by revolving a circle around an axis which does not intersect it. The figure we obtain is the torus or “inner tube” (denoted T ...
9 ページ
... compact since B,(x) is compact; thus M is locally compact. Because M has a countable base of open sets, we may now suppose that it has a countable base of relatively compact open sets {V}; obviously M = U V. Normality follows from ...
... compact since B,(x) is compact; thus M is locally compact. Because M has a countable base of open sets, we may now suppose that it has a countable base of relatively compact open sets {V}; obviously M = U V. Normality follows from ...
13 ページ
... compact, connected, orientable 2-manifold is homeomorphic to. Cylinder Twisted (mobius) bond (o) (b) Klein bottle (c) (d) Figure I.5 Four ways to identify sides of a rectangle: (a) cylinder; (b) twisted (Möbius) band; (c) torus; (d) ...
... compact, connected, orientable 2-manifold is homeomorphic to. Cylinder Twisted (mobius) bond (o) (b) Klein bottle (c) (d) Figure I.5 Four ways to identify sides of a rectangle: (a) cylinder; (b) twisted (Möbius) band; (c) torus; (d) ...
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