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.
内页插图
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 epub pdf mobi txt 电子书 下载 2024
莫尔斯理论 下载 epub mobi pdf txt 电子书 2024
评分
☆☆☆☆☆
宝贝又好又便宜,快递又快又周到,我们真正好开心!
评分
☆☆☆☆☆
不错的书,需要花时间看一看
评分
☆☆☆☆☆
1960年代的书,字体太难看了……看着累人,印刷也太差了。还不如买中文版的……
评分
☆☆☆☆☆
J.Milnor先生的小品作,买来观摩
评分
☆☆☆☆☆
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.
评分
☆☆☆☆☆
经典好书,值得购买!
评分
☆☆☆☆☆
milnor 的经典之作。
评分
☆☆☆☆☆
书还行吧,就是看不懂,全英文的!!
评分
☆☆☆☆☆
不错,活动时买的,挺划算的。