莫尔斯理论 下载 mobi epub pdf 电子书 2025

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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 下载 mobi epub pdf txt 电子书 格式

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有需要的可以看一看。

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米尔诺的Morse理论是本专著，虽然不厚，但是将Morse理论讲得很透彻，毕竟是大师之作啊

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经典必读书籍

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经典书籍，必读

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不错……………………………

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莫尔斯理论的经典教材，是本研究领域不可不读的教材

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不错……………………………

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真的很薄的的一本书。

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很好的一本数学书，推荐

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