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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ix ページ
... Derivatives 312 Vy, Y and Differentiation of Vector Fields 314 3. Differentiation on Riemannian Manifolds 317 Constant Vector Fields and Parallel Displacement 323 4. Addenda to the Theory of Differentiation on a Manifold 325 The ...
... Derivatives 312 Vy, Y and Differentiation of Vector Fields 314 3. Differentiation on Riemannian Manifolds 317 Constant Vector Fields and Parallel Displacement 323 4. Addenda to the Theory of Differentiation on a Manifold 325 The ...
xiii ページ
... derivatives, multiple integrals, and so on. Although in overall content this book necessarily overlaps the several available excellent books on manifold theory, there are differences in presentation and emphasis which, it is hoped, will ...
... derivatives, multiple integrals, and so on. Although in overall content this book necessarily overlaps the several available excellent books on manifold theory, there are differences in presentation and emphasis which, it is hoped, will ...
16 ページ
... 7 local coordinates of p relative to some coordinate neighborhood U. The 2-sphere S4 and some of its tangent vectors—elements of T(S*). the derivatives 6g/6x', ..., 6g/6x" all being evaluated at the. 16 I N T R O DUCTI O N TO MA N IF O L ...
... 7 local coordinates of p relative to some coordinate neighborhood U. The 2-sphere S4 and some of its tangent vectors—elements of T(S*). the derivatives 6g/6x', ..., 6g/6x" all being evaluated at the. 16 I N T R O DUCTI O N TO MA N IF O L ...
20 ページ
... derivatives from advanced calculus. Few proofs are given; they may be worked out as problems or found in advanced calculus texts, for example, Apostol [1], Dieudonnés 1], or Fleming [1]. We will consider real-valued functions 20 Chapter ...
... derivatives from advanced calculus. Few proofs are given; they may be worked out as problems or found in advanced calculus texts, for example, Apostol [1], Dieudonnés 1], or Fleming [1]. We will consider real-valued functions 20 Chapter ...
21 ページ
... derivatives are defined there. The natural generalization of existence of the derivative for functions of one variable is as follows. We shall say that f is differentiable at a e U if there is a (homogeneous) linear expression X - b,(x ...
... derivatives are defined there. The natural generalization of existence of the derivative for functions of one variable is as follows. We shall say that f is differentiable at a e U if there is a (homogeneous) linear expression X - b,(x ...
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