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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... notation that are used. Chapter II is largely advanced calculus and may very well be omitted or skimmed by better prepared readers. In Chapter III, the basic concept of differentiable manifold is introduced along with mappings of ...
... notation that are used. Chapter II is largely advanced calculus and may very well be omitted or skimmed by better prepared readers. In Chapter III, the basic concept of differentiable manifold is introduced along with mappings of ...
1 ページ
I INTRODUCTION TO MANIFOLDS In this chapter, we establish some preliminary notations and give an intuitive, geometric discussion of a number of examples of manifolds—the primary objects of study throughout the book. Most of these ...
I INTRODUCTION TO MANIFOLDS In this chapter, we establish some preliminary notations and give an intuitive, geometric discussion of a number of examples of manifolds—the primary objects of study throughout the book. Most of these ...
2 ページ
... notation to simplify things a bit, for example, to describe linear mappings, equations, and so on. Thus R" may denote a vector space of dimension n over R. We sometimes mean even more by R". An abstract n-dimensional vector space over R ...
... notation to simplify things a bit, for example, to describe linear mappings, equations, and so on. Thus R" may denote a vector space of dimension n over R. We sometimes mean even more by R". An abstract n-dimensional vector space over R ...
3 ページ
... notation is frequently useful even when we are dealing with R" as a metric space and not using its vector space structure. Note, in particular, that |x|= d(x,0), the distance from the point x to the origin. In this equality x is a ...
... notation is frequently useful even when we are dealing with R" as a metric space and not using its vector space structure. Note, in particular, that |x|= d(x,0), the distance from the point x to the origin. In this equality x is a ...
6 ページ
... notation dim M is used for the dimension of M ; when dim M = 0, then M is a countable space with the discrete topology. It follows from the homeomorphism of U and U' that locally Euclidean is equivalent to the requirement that each ...
... notation dim M is used for the dimension of M ; when dim M = 0, then M is a countable space with the discrete topology. It follows from the homeomorphism of U and U' that locally Euclidean is equivalent to the requirement that each ...
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