An Introduction to Differentiable Manifolds and Riemannian GeometryAcademic Press, 1986/04/21 - 429 ページ An Introduction to Differentiable Manifolds and Riemannian Geometry |
この書籍内から
検索結果1-5 / 86
xiv ページ
... corresponding geometry is used to prove that every element lies on a one-parameter subgroup. In the last two chapters, which deal with Riemannian geometry of abstract n-dimensional manifolds, the relation to the more easily visualized ...
... corresponding geometry is used to prove that every element lies on a one-parameter subgroup. In the last two chapters, which deal with Riemannian geometry of abstract n-dimensional manifolds, the relation to the more easily visualized ...
3 ページ
... corresponding point on the right-hand side; an illustration of the way various interpretations of R" can be mixed together. Exercises 1. Show that if A is an m x n matrix, then the mapping from V" to V" (with elements written as n x 1 ...
... corresponding point on the right-hand side; an illustration of the way various interpretations of R" can be mixed together. Exercises 1. Show that if A is an m x n matrix, then the mapping from V" to V" (with elements written as n x 1 ...
4 ページ
... corresponding one in R*. It is the existence of such coordinate mappings which make the identification of E* and R* possible. But caution! An arbitrary choice of coordinates is involved, there is no natural, geometrically determined way ...
... corresponding one in R*. It is the existence of such coordinate mappings which make the identification of E* and R* possible. But caution! An arbitrary choice of coordinates is involved, there is no natural, geometrically determined way ...
6 ページ
... corresponding sides are of equal length. 3 Topological Manifolds Of all the spaces which one studies in topology the Euclidean spaces and their subspaces are the most important. As we have just seen, the metric spaces R" serve as a ...
... corresponding sides are of equal length. 3 Topological Manifolds Of all the spaces which one studies in topology the Euclidean spaces and their subspaces are the most important. As we have just seen, the metric spaces R" serve as a ...
7 ページ
... corresponding ambient Euclidean space. Thus in the case of So we identify R* and E°, and So becomes the unit sphere centered at the origin. At each point p of So we have a tangent plane and a unit normal vector N,. There will be a ...
... corresponding ambient Euclidean space. Thus in the case of So we identify R* and E°, and So becomes the unit sphere centered at the origin. At each point p of So we have a tangent plane and a unit normal vector N,. There will be a ...
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