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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... product (x, y) = Xxy. It is characterized by the fact that relative to this inner product the natural basis is orthonormal, (ei, ej) = 6;. Thus at times R" is a Euclidean vector space, but 2 | | N T R O DUCTION TO M A N F O L DS.
... product (x, y) = Xxy. It is characterized by the fact that relative to this inner product the natural basis is orthonormal, (ei, ej) = 6;. Thus at times R" is a Euclidean vector space, but 2 | | N T R O DUCTION TO M A N F O L DS.
3 ページ
... orthonormal basis and inner product. An abstract vector space, even if Euclidean, does not have any such preferred ... orthonormal basis. 8. Prove that every Euclidean vector space V has an orthonormal basis. Construct your proof in such ...
... orthonormal basis and inner product. An abstract vector space, even if Euclidean, does not have any such preferred ... orthonormal basis. 8. Prove that every Euclidean vector space V has an orthonormal basis. Construct your proof in such ...
18 ページ
... orthonormal pairs of vectors in V* (Exercise 3) is homeomorphic to To(S*), the tangent sphere bundle of So, which consists of all unit vectors tangent to So. 5. Let C be a one-dimensional manifold (curve) in R*. Show that the collection ...
... orthonormal pairs of vectors in V* (Exercise 3) is homeomorphic to To(S*), the tangent sphere bundle of So, which consists of all unit vectors tangent to So. 5. Let C be a one-dimensional manifold (curve) in R*. Show that the collection ...
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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