莫爾斯理論

內(nèi)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.

作者簡(jiǎn)介

作者：(美國)米爾諾 (J.Milnor)

書籍目錄

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

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