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 / 42
vii ページ
... Rank of a Mapping 46 IV. Vector Fields on a Manifold The Tangent Space at. III. Notes 50 Differentiable Manifolds and Submanifolds The Definition of a Differentiable Manifold 52 Further Examples 60 Differentiable Functions and Mappings 65 ...
... Rank of a Mapping 46 IV. Vector Fields on a Manifold The Tangent Space at. III. Notes 50 Differentiable Manifolds and Submanifolds The Definition of a Differentiable Manifold 52 Further Examples 60 Differentiable Functions and Mappings 65 ...
20 ページ
... rank. (Many readers can skim over or skip this chapter entirely.) Briefly, the topics treated are the following: In Section 1 we define differentiability of real-valued functions of many variables and its immediate consequences, in ...
... rank. (Many readers can skim over or skip this chapter entirely.) Briefly, the topics treated are the following: In Section 1 we define differentiability of real-valued functions of many variables and its immediate consequences, in ...
28 ページ
... rank of the product of two matrices is less than or equal to the rank of either factor. Show that multiplying a matrix on the left or right by a nonsingular matrix does not change its rank. ! Just as in the case of functions, we can ...
... rank of the product of two matrices is less than or equal to the rank of either factor. Show that multiplying a matrix on the left or right by a nonsingular matrix does not change its rank. ! Just as in the case of functions, we can ...
46 ページ
... Rank of a Mapping In linear algebra the rank of an m x n matrix A is defined in three equivalent ways: (i) the dimension of the subspace of V" spanned by the rows, (ii) the dimension of the subspace of V" spanned by the columns, and ...
... Rank of a Mapping In linear algebra the rank of an m x n matrix A is defined in three equivalent ways: (i) the dimension of the subspace of V" spanned by the rows, (ii) the dimension of the subspace of V" spanned by the columns, and ...
47 ページ
... rank A s m, n. The rank of a linear transformation is defined to be the dimension of the image, and one proves that this is the rank of any matrix which represents the transformation. From this it follows that, if P and Q are ...
... rank A s m, n. The rank of a linear transformation is defined to be the dimension of the image, and one proves that this is the rank of any matrix which represents the transformation. From this it follows that, if P and Q are ...
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