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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... 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 and m ... Exercise 1 to be onto; to be Orle-to-One. 3. Show that if W is an n-dimensional Euclidean vector space, then there ...
... 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 and m ... Exercise 1 to be onto; to be Orle-to-One. 3. Show that if W is an n-dimensional Euclidean vector space, then there ...
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... exercise the proof that these are manifolds. Thus to generate new 2manifolds from old ones we may (1) cut out two disks, leaving a manifold M whose boundary 6M is the disjoint union of two circles, and (2) paste on a cylinder or “handle ...
... exercise the proof that these are manifolds. Thus to generate new 2manifolds from old ones we may (1) cut out two disks, leaving a manifold M whose boundary 6M is the disjoint union of two circles, and (2) paste on a cylinder or “handle ...
18 ページ
... Exercises 1. Show that P*(R) and the manifold of Exercise 4.4 are homeomorphic. Show that P*(R) and the set of all planes through the origin of R* are in natural one-to-one correspondence. 3. Show that the set of all pairs (x, y) of ...
... Exercises 1. Show that P*(R) and the manifold of Exercise 4.4 are homeomorphic. Show that P*(R) and the set of all planes through the origin of R* are in natural one-to-one correspondence. 3. Show that the set of all pairs (x, y) of ...
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... exercise. Using it we may establish the mean value theorem for functions of several variables. We shall say that a domain U is starlike with respect to a e U provided that whenever xe U, then the segment ax lies entirely in U (see Fig ...
... exercise. Using it we may establish the mean value theorem for functions of several variables. We shall say that a domain U is starlike with respect to a e U provided that whenever xe U, then the segment ax lies entirely in U (see Fig ...
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... exercise. 1/2 |g(x) – g(a)|= Therefore ye-ay". (1.7) Corollary If f is of class C" on U, then at any point of U the ... Exercises Prove (1.1). Prove (1.3) using the mean value theorem 24 | | FUN CTI O N S OF S E V E R A L VA R A B L ES ...
... exercise. 1/2 |g(x) – g(a)|= Therefore ye-ay". (1.7) Corollary If f is of class C" on U, then at any point of U the ... Exercises Prove (1.1). Prove (1.3) using the mean value theorem 24 | | FUN CTI O N S OF S E V E R A L VA R A B L ES ...
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