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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... components of the unit normal vector depend continuously on the point p.) This smoothness allows us to prove the locally Euclidean property by projection of a neighborhood of p onto a plane as in Examples 3.3 and 3.4. The other ...
... components of the unit normal vector depend continuously on the point p.) This smoothness allows us to prove the locally Euclidean property by projection of a neighborhood of p onto a plane as in Examples 3.3 and 3.4. The other ...
11 ページ
... components of a manifold M are open sets and are countable in number. 4 Further Examples of Manifolds. Cutting and Pasting A hemispherical cap (including the equator) or a right circular cylinder (including the circles at the ends) are ...
... components of a manifold M are open sets and are countable in number. 4 Further Examples of Manifolds. Cutting and Pasting A hemispherical cap (including the equator) or a right circular cylinder (including the circles at the ends) are ...
12 ページ
... components by a homeomorphism, assuming of course the necessary condition that such components are homeomorphic. The simplest examples are S*, which is obtained by pasting two disks (or hemispheres) together so as to form the equator ...
... components by a homeomorphism, assuming of course the necessary condition that such components are homeomorphic. The simplest examples are S*, which is obtained by pasting two disks (or hemispheres) together so as to form the equator ...
17 ページ
... components which determine X, relative to some basis {E1, E2, of T.(M), a basis which varies continuously over the neighborhood U. We later make these statements quite precise and in so doing exhibit the locally Euclidean character of T ...
... components which determine X, relative to some basis {E1, E2, of T.(M), a basis which varies continuously over the neighborhood U. We later make these statements quite precise and in so doing exhibit the locally Euclidean character of T ...
30 ページ
... components relative to the basis E1a, ..., Ena, which in turn are given by subtracting from the coordinates of the terminal point of each vector, the coordinates of its initial point a. The geometry of E" has guided us to a proper ...
... components relative to the basis E1a, ..., Ena, which in turn are given by subtracting from the coordinates of the terminal point of each vector, the coordinates of its initial point a. The geometry of E" has guided us to a proper ...
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