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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ix ページ
... Plane Curves 305 2. Differentiation of Vector Fields on Submanifolds of R" 307 Formulas for Covariant Derivatives 312 Vy, Y and Differentiation of Vector Fields 314 3. Differentiation on Riemannian Manifolds 317 Constant Vector Fields ...
... Plane Curves 305 2. Differentiation of Vector Fields on Submanifolds of R" 307 Formulas for Covariant Derivatives 312 Vy, Y and Differentiation of Vector Fields 314 3. Differentiation on Riemannian Manifolds 317 Constant Vector Fields ...
1 ページ
... plane and in space—were the original objects of study in classical differential geometry and are the source of much of the current theory. The first two sections deal primarily with notational matters and the relation between Euclidean ...
... plane and in space—were the original objects of study in classical differential geometry and are the source of much of the current theory. The first two sections deal primarily with notational matters and the relation between Euclidean ...
5 ページ
... plane not through the origin? If we wish to prove the theorems of Euclidean geometry by analytical geometry methods, we need to define the notion of congruence. We say that two figures are congruent if there is a rigid motion of the ...
... plane not through the origin? If we wish to prove the theorems of Euclidean geometry by analytical geometry methods, we need to define the notion of congruence. We say that two figures are congruent if there is a rigid motion of the ...
7 ページ
... plane and a unit normal vector N,. There will be a coordinate axis which is not perpendicular to N, and some neighborhood U of p on So will then project in a continuous and one-to-one fashion onto an open set U" of the coordinate plane ...
... plane and a unit normal vector N,. There will be a coordinate axis which is not perpendicular to N, and some neighborhood U of p on So will then project in a continuous and one-to-one fashion onto an open set U" of the coordinate plane ...
8 ページ
... plane as illustrated. Since we use the relative topology derived from E°, the space To is necessarily Hausdorff and has a countable basis of open sets. Thus conditions (i)-(iii) of Definition 3.1 are satisfied. (3.5) Remark It should be ...
... plane as illustrated. Since we use the relative topology derived from E°, the space To is necessarily Hausdorff and has a countable basis of open sets. Thus conditions (i)-(iii) of Definition 3.1 are satisfied. (3.5) Remark It should be ...
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