莫尔斯理论

出版时间：2011-7  出版社：世界图书出版公司  作者：John Milnor  页数：153  
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内容概要

　　This book gives a present-day account of Marston Morse's theory of the calculus of variations in the large. However, there have been Im-portant developments during the past few years which are not mentioned.Let me describe three of these.

作者简介

作者：(美国)米尔诺 (J.Milnor)

书籍目录

PREFACEPART 1 NON-DEGENERATE SMOOTH FUNCTIONS ON A MANIFOLDIntroductionDefinitions and LenmmsHomotopy Type in TeRns of Critical ValuesExamplesThe Morse InequalitiesManifolds in Euclidean Space: The Existence of Non-degenerate FunctionsThe Lefschetz Theorem on Hyperplane SectionsPART 2 A RAPID COURSE IN RIEMANNIAN GEOMETRYCovariant DifferentiationThe Curvature TensorGeodesics and CompletenessPART 3 THE CALCULUS OF VARIATIONS APPLIED TO GEODESICSThe Path Space of a Smooth ManifoldThe Fnergy of a PathThe Hessian of the Energy Function at a Critical Path Jacobi Fields: The Null-space of E**The Index TheoremA Finite Dimensional Approximation to ncThe Topology of the Full Path SpaceExistence of Non-conjugate PointsSome Between Topology and CurvaturePART 4 APPLICATIONS TO LIE GROUPS AND SYMMEIRIC SPACESSymmetric SpacesLie Groups as Symmetric SpacesWhole Manifolds of Minimal GeodesicsThe Bott Periodicity Theorem for the Unitary GroupThe Periodicity Theorem for the Orthogonal GroupAPPENDIX THE HOMOTOPY TYPE OF A MONOTONE UNION

章节摘录

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《莫尔斯理论(英文)》由世界图书出版公司出版。

用户评论 (总计2条)

•   Milnor写得书向来以文笔优美著称，本书尤为如此，特别是他用很短的篇幅给黎曼几何做了一个非常漂亮的导论，而本书第一面的那个图，怕更是被引用无数次。
•   这不用说，数学人都懂得！