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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... matrix groups, and certain quotient manifolds are introduced early and used throughout as examples. A fairly large number of problems (almost 400) is included to develop intuition and computational skills. Further, it may be said that ...
... matrix groups, and certain quotient manifolds are introduced early and used throughout as examples. A fairly large number of problems (almost 400) is included to develop intuition and computational skills. Further, it may be said that ...
2 ページ
... matrices, and at other times as columns, that is, n x 1 matrices. This only becomes important should we wish to use matrix notation to simplify things a bit, for example, to describe linear mappings, equations, and so on. Thus R" may ...
... matrices, and at other times as columns, that is, n x 1 matrices. This only becomes important should we wish to use matrix notation to simplify things a bit, for example, to describe linear mappings, equations, and so on. Thus R" may ...
3 ページ
... matrices over R and the vector space R”. Show that the map X → AX, where A is a fixed m × m matrix and X is an arbitrary m x n matrix (over R), is continuous in the topology derived from R". 6. Show that |x| has the following ...
... matrices over R and the vector space R”. Show that the map X → AX, where A is a fixed m × m matrix and X is an arbitrary m x n matrix (over R), is continuous in the topology derived from R". 6. Show that |x| has the following ...
24 ページ
... matrices of determinant zero (which have no inverses), then each entry in the inverse A of a matrix a is an analytic (and hence C*) function of the entries in the matrix A. Exercises Prove (1.1). Prove (1.3) using the mean value theorem ...
... matrices of determinant zero (which have no inverses), then each entry in the inverse A of a matrix a is an analytic (and hence C*) function of the entries in the matrix A. Exercises Prove (1.1). Prove (1.3) using the mean value theorem ...
26 ページ
... matrix of . of àxf ax" Č(f'.....s") . - ô(x', ..., x") - - of . of axi ax" is defined at each point of U, its mn entries being functions on U. These functions need not be continuous on U; they are so if and only if F is of class C ...
... matrix of . of àxf ax" Č(f'.....s") . - ô(x', ..., x") - - of . of axi ax" is defined at each point of U, its mn entries being functions on U. These functions need not be continuous on U; they are so if and only if F is of class C ...
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