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内容简介

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.

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目录

PREFACE
PART 1 NON-DEGENERATE SMOOTH FUNCTIONS ON A MANIFOLD
Introduction
Definitions and Lenmms
Homotopy Type in TeRns of Critical Values
Examples
The Morse Inequalities
Manifolds in Euclidean Space: The Existence of Non-degenerate Functions
The Lefschetz Theorem on Hyperplane Sections

PART 2 A RAPID COURSE IN RIEMANNIAN GEOMETRY
Covariant Differentiation
The Curvature Tensor
Geodesics and Completeness

PART 3 THE CALCULUS OF VARIATIONS APPLIED TO GEODESICS
The Path Space of a Smooth Manifold
The Fnergy of a Path
The Hessian of the Energy Function at a Critical Path
Jacobi Fields: The Null-space of E**
The Index Theorem
A Finite Dimensional Approximation to nc
The Topology of the Full Path Space
Existence of Non-conjugate Points
Some Between Topology and Curvature

PART 4 APPLICATIONS TO LIE GROUPS AND SYMMEIRIC SPACES
Symmetric Spaces
Lie Groups as Symmetric Spaces
Whole Manifolds of Minimal Geodesics
The Bott Periodicity Theorem for the Unitary Group
The Periodicity Theorem for the Orthogonal Group
APPENDIX THE HOMOTOPY TYPE OF A MONOTONE UNION

前言/序言

莫尔斯理论 电子书 下载 mobi epub pdf txt

评分☆☆☆☆☆

很好的一本数学书，推荐

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Milnor 的经典之作！

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如果有兴趣了解莫尔斯理论的，可以参考

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经典好书，值得购买！

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不错……………………………

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这本书是Morse理论的经典著作，作者书准极高

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J.Milnor ，世界著名数学家，1962年菲尔兹奖获得者1989年沃尔夫奖获得者。Morse理论作为变分学里面的重要一部分，已被应用到许多数学分支，我国著名数学家北京大学张恭庆院士将其推广至无穷维。

评分☆☆☆☆☆

非常棒，经典著作，值得购买！

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春色满园关不住，一枝红杏出墙来

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