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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viii ページ
... Element 215 8. Exterior Differentiation 219 An Application to Frobenius' Theorem 223 Notes 227 VI. Integration on Manifolds 8. Some Further Applications of de Rham Groups 281 The. 1. Integration in R*. Domains of Integration 230 Basic ...
... Element 215 8. Exterior Differentiation 219 An Application to Frobenius' Theorem 223 Notes 227 VI. Integration on Manifolds 8. Some Further Applications of de Rham Groups 281 The. 1. Integration in R*. Domains of Integration 230 Basic ...
xiv ページ
... element lies on a one-parameter subgroup. In the last two chapters, which deal with Riemannian geometry of abstract n-dimensional manifolds, the relation to the more easily visualized geometry of curves and surfaces in Euclidean space ...
... element lies on a one-parameter subgroup. In the last two chapters, which deal with Riemannian geometry of abstract n-dimensional manifolds, the relation to the more easily visualized geometry of curves and surfaces in Euclidean space ...
3 ページ
... elements written as n x 1 and m × 1 matrices), which is defined by y = Ax, is continuous. Identify the images of the canonical basis of V" as linear combinations of the canonical basis of V". 2. Find conditions for the mapping of ...
... elements written as n x 1 and m × 1 matrices), which is defined by y = Ax, is continuous. Identify the images of the canonical basis of V" as linear combinations of the canonical basis of V". 2. Find conditions for the mapping of ...
4 ページ
... elements, for example, lines of E° with subsets of R* consisting of the solutions of linear equations. Thus we carry each geometric object to a corresponding one in R*. It is the existence of such coordinate mappings which make the ...
... elements, for example, lines of E° with subsets of R* consisting of the solutions of linear equations. Thus we carry each geometric object to a corresponding one in R*. It is the existence of such coordinate mappings which make the ...
12 ページ
... to obtain surfaces. Figure I.5 illustrates this: we obtain a cylinder, Möbius band, torus, and. Figure 1.4 Some examples of pasting. The 2-sphere S4 and some of its tangent vectors—elements of. 12 I INT R O DUCTIO N TO MA N IF O L DS.
... to obtain surfaces. Figure I.5 illustrates this: we obtain a cylinder, Möbius band, torus, and. Figure 1.4 Some examples of pasting. The 2-sphere S4 and some of its tangent vectors—elements of. 12 I INT R O DUCTIO N TO MA N IF O L DS.
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