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
... Surfaces in E° 366 The Principal Curvatures at a Point of a Surface 370 2. The Gaussian and Mean Curvatures of a Surface 374 The Theorema Egregium of Gauss 377 Basic Properties of the Riemann Curvature Tensor 382 The Curvature Forms and ...
... Surfaces in E° 366 The Principal Curvatures at a Point of a Surface 370 2. The Gaussian and Mean Curvatures of a Surface 374 The Theorema Egregium of Gauss 377 Basic Properties of the Riemann Curvature Tensor 382 The Curvature Forms and ...
xiii ページ
... surface integrals, divergence and curl of vector fields, and Stokes's and Green's theorems find their most natural setting in manifold theory. But however natural the leap from calculus on domains of Euclidean space to calculus on ...
... surface integrals, divergence and curl of vector fields, and Stokes's and Green's theorems find their most natural setting in manifold theory. But however natural the leap from calculus on domains of Euclidean space to calculus on ...
xiv ページ
... surfaces, and so on. Finally, it should be said that the author has tried to include at every stage results that illustrate the power of these ideas. Chapter VI is especially noteworthy in this respect in that it includes complete ...
... surfaces, and so on. Finally, it should be said that the author has tried to include at every stage results that illustrate the power of these ideas. Chapter VI is especially noteworthy in this respect in that it includes complete ...
xv ページ
... surfaces in Euclidean space, the concept of Riemannian connection and covariant differentiation is carefully developed and used to give a fairly extensive discussion of geodesics— including the Hopf–Rinow theorem—and a shorter treatment ...
... surfaces in Euclidean space, the concept of Riemannian connection and covariant differentiation is carefully developed and used to give a fairly extensive discussion of geodesics— including the Hopf–Rinow theorem—and a shorter treatment ...
1 ページ
... surfaces in Euclidean space; for these—together with curves on the plane and in space—were the original objects of study in classical differential geometry and are the source of much of the current theory. The first two sections deal ...
... surfaces in Euclidean space; for these—together with curves on the plane and in space—were the original objects of study in classical differential geometry and are the source of much of the current theory. The first two sections deal ...
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