0去购物车结算
购物车中还没有商品,赶紧选购吧!
当前位置: 图书分类 > 数学 > 几何/拓扑 > 几何IV:非正规黎曼几何

浏览历史

几何IV:非正规黎曼几何


联系编辑
 
标题:
 
内容:
 
回执地址:
 
  
几何IV:非正规黎曼几何
  • 书号:9787030235015
    作者:Reshetnyak
  • 外文书名:Geometry Ⅳ:Non-regular Riemannian Geometry
  • 丛书名:国外数学名著系列(影印版)
  • 装帧:精装
    开本:B5
  • 页数:264
    字数:315000
    语种:英文
  • 出版社:科学出版社
    出版时间:2009-01
  • 所属分类:O18 几何、拓扑
  • 定价: ¥60.00元
    售价: ¥48.00元
  • 图书介质:
    纸质书

  • 购买数量: 件  缺货,请选择其他介质图书!
  • 商品总价:

相同系列
全选

内容介绍

样章试读

用户评论

全部咨询

This volume of the Encyclopaedia contains two articles which give a survey of modem research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians.
The first article written by Reshetnyak is devoted to the theory of two-dimensional Riemannian manifolds of bounded curvature. Concepts of Riemannian geometry such as the area and integral curvature of a set and the length and integral curvature of a curve are also defined for these manifolds. Some fundamental results of Riemannian geometry like the Gauss-Bonnet formula are true in the more general case considered in the book.
The second article by Berestovskij and Nikolaev is devoted to the theory of metric spaces whose curvature lies between two given constants. The main result is that these spaces are in fact Riemannian. This result has important applications in global Riemannian geometry.
Both parts cover topics which have not yet been treated in monograph form. Hence the book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry.
样章试读
  • 暂时还没有任何用户评论
总计 0 个记录,共 1 页。 第一页 上一页 下一页 最末页

全部咨询(共0条问答)

  • 暂时还没有任何用户咨询内容
总计 0 个记录,共 1 页。 第一页 上一页 下一页 最末页
用户名: 匿名用户
E-mail:
咨询内容:

目录

  • Ⅰ Two-Dimensional Manifolds of Bounded Curvature
    Chapter 1 Preliminary Information
    §1. Introduction
    1.1. General Information about the Subject of Research and a Survey of Results
    1.2. Some Notation and Terminology
    §2. The Concept of a Space with Intrinsic Metric
    2.1. The Concept of the Length of a Parametrized Curve
    2.2. A Space with Intrinsic Metric.The Induced Metric
    2.3. The Concept of a Shortest Curve
    2.4. The Operation of Cutting of a Space with Intrinsic Metric
    §3. Two-Dimensional Manifolds with Intrinsic Metric
    3.1. Definition.Triangulation of a Manifold
    3.2. Pasting of Two-Dimensional Manifolds with Intrinsic Metric
    3.3. Cutting of Manifolds
    3.4. A Side of a Simple Arc in a Two-Dimensional Manifold
    §4. Two-Dimensional Riemannian Geometry
    4.1. Differentiable Two-Dimensional Manifolds
    4.2. The Concept of a Two-Dimensional Riemannian Manifold
    4.3. The Curvature of a Curve in a Riemannian Manifold.Integral Curvature.The Gauss-Bonnet Formula
    4.4. Isothermal Coordinates in Two-Dimensional Riemannian Manifolds of Bounded Curvature
    §5. Manifolds with Polyhedral Metric
    5.1. Cone and Angular Domain
    5.2. Definition of a Manifold with Polyhedral Metric
    5.3. Curvature of a Set on a Polyhedron.Turn of the Boundary.I'he Gauss-Bonnet Theorem
    5.4. A Turn of a Polygonal Line on a Polyhedron
    5.5. Characterization of the Intrinsic Geometry of Convex Polyhedra
    5.6. An Extremal Property of a Convex Cone.The Method of Cutting and Pasting as a Means of Solving Extremal Problems for Polyhedra
    5.7. The Concept of a K-Polyhedron
    Chapter 2 Different Ways of Defining Two-Dimensional Manifolds of Bounded Curvature
    §6. Axioms of a Two-Dimensional Manifold of Bounded Curvature.Characterization of such Manifolds by Means of Approximation by Polyhedra
    6.1. Axioms of a Two-Dimensional Manifold of Bounded Curvature
    6.2. Theorems on the Approximation of Two-Dimensional Manifolds of Bounded Curvature by Manifolds with Polyhedral and Riemannian Metric
    6.3. Proof of the First Theorem on Approximation
    6.4. Proof of Lemma 6.3.1
    6.5. Proof of the Second Theorem on Approximation
    §7. Analytic Characterization of Two-Dimensional Manifolds of Bounded Curvature
    7.1. Theorems on Isothermal Coordinates in a Two-Dimensional Manifold of Bounded Curvature
    7.2. Some Information about Curves on a Plane and in a Riemannian manifold
    7.3. Proofs of Theorems 7.1.1,7.1.2,7.1.3
    7.4. On the ProofofTheorem 7.3.1
    Chapter 3 Basic Facts of the Theory of Manifolds of Bounded Curvature
    §8. Basic Results of the Theory of Two-Dimensional Manifolds of Bounded Curvature
    8.1. A Turn of a Curve and the Integral Curvature of a Set
    8.2. A Theorem on the Contraction of a Cone.Angle between Curves.Comparison Theorems
    8.3. A Theorem on Pasting Together Two-Dimensional Manifolds of Bounded Curvature
    8.4. Theorems on Passage to the Limit for Two-Dimensional Manifolds of Bounded Curvature
    8.5. Some Inequalities and Estimates.Extremal Problems for Two-Dimensional Manifolds of Bounded Curvature
    §9. Further Results.Some Additional Remarks
    References
    Ⅱ Multidimensional Generalized Riemannian Spaces
    Introduction
    0.1. RiemannianSpaces
    0.2. Generalized Riemannian Spaces
    0.3. Riemannian Geometry and Generalized Riemannian Spaces
    0.4. A Brief Characterization of the Article by Chapters
    0.5. In What Sense Do the Stated Results Have Multidimensional Character?
    0.6. Final Remarks on the Text
    Chapter 1 Basic Concepts Connected with the Intrinsic Metric
    §1 Intrinsic Metric.Shortest Curve.Triangle.Angle.Excess of a Triangle
    1.1. Intrinsic Metric
    1.2. Shortest Curve
    1.3. Triangle
    1.4. Angle
    1.5. Excess
    §2. General Propositions about Upper Angles
    §3. The Space of Directions at a Point.K-Cone.Tangent Space
    3.1. Direction
    3.2. K-Cone
    3.3. Tangent Space
    §4. Remarks.Examples
    4.1. Intrinsic Metric.Shortest Curve.Angles
    4.2. An Assertion Completely Dual to Theorem 2.1,that is.the Corresponding Lower Bound for the Lower Angle Does not Hold
    4.3. Tangent Space.Space of Directions
    Chapter 2 Spaces of Curvature ≤ K (and ≥K')
    §5. Spaces of Curvature ≤ K.The Domain RK,and its Basic Properties
    5.1. Definition of a Space of Curvature ≤ K
    5.2. Basic Properties of the Domain RK
    5.3. The Domain PK
    §6. The Operation of Gluing
    6.1. Gluing of Metric Spaces with Intrinsic Metric
    §7. Equivalent Definitions of Upper Boundedness of the Curvature
    7.1. Conditions under which a Space of Curvature ≤ K is the Domain RK
    7.2. Connection with the Riemannian Definition of Curvature
    7.3. Definition of Upper Boundedness of Curvature
    7.4. Non-Expanding Maps in Spaces of Curvature ≤ K
    7.5. Boundedness of the Curvature from the Viewpoint of Distance Geometry
    §8. Space of Directions,Tangent Space at a Point of a Space of Curvature ≤ K
    8.1. Conditions under which a Shortest Curve Goes out in each Direction
    8.2. Intrinsic Metric in Ωp
    8.3. Tangent Space
    §9. Surfaces and their Areas
    9.1. The Definition of the Area of a Surface
    9.2. Properties of Area
    9.3. Ruled Surfaces in RK
    9.4. Isoperimetric Inequality
    9.5. Plateau's Problem
    §10. Spaces of Curvature both ≤ K and ≥ K'
    10.1. Definition of a Space of Curvature both ≤ K and ≥ K'
    10.2. Basic Properties of a Domain RK'.K
    10.3. Equivalent Definitions of Boundedness of Curvature
    §11. Remarks,Examples
    11.1. Spaces of Curvature ≤ K as a Generalization of Riemannian Spaces
    11.2. Polyhedral Metrics
    11.3. Spaces of Curvature ≥ K'
    Chapter 3 Spaces with Bounded Curvature
    §12. CO-RiemannianS tructure in Spaces with Bounded Curvature
    12.1. Definition of a Space with Bounded Curvature
    12.2. The Tangent Space at a Point of a Space with Bounded Curvature
    12.3. Introduction of CO-Smooth Riemannian Structure
    §13. Parallel Translation in Spaces with Bounded Curvature
    13.1. Construction of a Parallel Translation
    13.2. Statement of the Main Results
    13.3. Plan of the Proof of the Main Results of §13
    §14. Smoothness of the Metric of Spaces with Bounded Curvature
    14.1. Statement of the Main Result
    14.2. Plan of the Proof of Theorem 14.1
    §15. Spaces with Bounded Curvature and Limits of Smooth Riemannian Metrics
    15.1. Approximation of the Metric of a Space with Bounded Curvature by Smooth Riemannian Metrics
    15.2. A Space of Riemannian Manifolds with Sectional Curvatures Bounded in Aggregate
    Chapter 4 Existence of the Curvature of a Metric Space at a Point and the Axioms of Riemannian Geometry
    §16. The Space of Directions of an Arbitrary Metric Space
    16.1. Distance between Directions
    16.2. Space of Directions
    §17. Curvature of a Metric Space
    17.1. Definition of Non-isotropic Riemannian Curvature
    17.2. Existence of Curvature at a Point
    17.3. Geometrical Meaning of Sectional Curvature
    17.4. Isotropic Riemannian Curvature
    17.5. Wald Curvature and its Connection with Isotropic Riemannian Curvature
    17.6. Continuity of Curvature
    §18. Axioms of Riemannian Geometry
    18.1. Synthetic Description of C2,α-Smooth Riemannian Manifolds
    18.2. Synthetic Description of Cm,α-Smooth Riemannian Manifolds(m=3,4,...)
    18.3. Isotropic Metric Spaces
    References
    Author Index
    Subject Index
帮助中心
公司简介
联系我们
常见问题
新手上路
发票制度
积分说明
购物指南
配送方式
配送时间及费用
配送查询说明
配送范围
快递查询
售后服务
退换货说明
退换货流程
投诉或建议
经营资质
营业执照
出版社经营许可证