莫尔斯理论

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米尔诺(J.Milnor) 著
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出版社: 世界图书出版公司
ISBN:9787510037481
版次:1
商品编码:10914296
包装:平装
开本:24开
出版时间:2011-07-01
页数:153
正文语种:英文

具体描述

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



用户评价

评分

商品名称:莫尔斯理论

评分

米尔诺的经典名著,数学写作的典范!

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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。

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商品名称:莫尔斯理论

评分

非常好,不错不错。。。

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春色满园关不住,一枝红杏出墙来

评分

数学名著,非常经典,推荐

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不错的书,需要花时间看一看

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