国外数学名著系列55:几何1
图书信息
出版社: 科学出版社; 第1版 (2009年1月1日)
丛书名: 国外数学名著系列(续一)(影印版)55
精装: 264页
正文语种: 简体中文
开本: 16
ISBN: 9787030234988
条形码: 9787030234988
尺寸: 24 x 17 x 1.8 cm
重量: 581 g
作者简介
作者:(俄罗斯)加姆克列利泽 (Gamkrelidze R.V.)
内容简介
《国外数学名著系列(续1)(影印版)55:几何1(微分几何基本思想与概念)》主要内容:Since the early work of Gauss and Riemann, differential geometry has grown into a vast network of ideas and approaches, encompassing local considerations such as differential invariants and jets as well as global ideas, such as Morse theory and characteristic classes. In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geometry. The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry. As an overview of the major current methods of differential geometry, EMS 28 is a map of these different ideas which explains the interesting points at every stop. The authors'' intention is that the reader should gain a new understanding of geometry from the process of reading this survey.
目录
Preface
Chapter1.Introduction:AMetamathematicalViewofDifferentialGeometry
1.AlgebraandGeometry-theDualityoftheIntellect
2.TwoExamples:AlgebraicGeometry,PropositionalLogicandSetTheory
3.OntheHistoryofGeometry
4.DifferentialCalculusandCommutativeAlgebra
5.WhatisDifferentialGeometry?
Chapter2.TheGeometryofSurfaces
Chapter3.TheFieldApproachofRiemann
Chapter4.TheGroupApproachofLieandKlein.TheGeometryofTransformationGroups
Chapter5.TheGeometryofDifferentialEquations
Chapter6.GeometricStructures
Chapter7.TheEquivalenceProblem,DifferentialInvariantsandPseudogroups
Chapter8.GlobalAspectsofDifferentialGeometry
CommentaryontheReferences
References
AuthorIndex
SubjectIndex