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III:曲面理论

相同作者的商品

浏览历史

几何III:曲面理论


联系编辑
 
标题:
 
内容:
 
回执地址:
 
  
几何III:曲面理论
  • 书号:9787030235008
    作者:Burago
  • 外文书名:Geometry Ⅲ:Theory of Surfaces
  • 丛书名:国外数学名著系列(影印版)
  • 装帧:精装
    开本:B5
  • 页数:268
    字数:323000
    语种:英文
  • 出版社:科学出版社
    出版时间:2009-01
  • 所属分类:
  • 定价: ¥99.00元
    售价: ¥99.00元
  • 图书介质:
    按需印刷

  • 购买数量: 件  可供
  • 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

The theory of surfaces in Euclidean spaces is remarkably rich in deep results and applications. This volume of the Encyclopaedia is concerned mainly with the connection between the theory of embedded surfaces and Riemannian geometry and with the geometry of surfaces as influenced bv intrinsic metrics.
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. The Geometry of Surfaces in Euclidean Spaces
    Preface
    Chapter 1 The Geometry of Two-Dimensional Manifolds and Surfaces in En
    §1. Statement of the Problem
    1.1. Classes of Metrics and Classes of Surfaces. Geometric Groups and Geometric Properties
    §2. Smooth Surfaces
    2.1. Types of Points
    2.2. Classes of Surfaces
    2.3. Classes of Metrics
    2.4 G-Connectedness
    2.5. Results and Conjectures
    2.6. The Conformal Group
    §3. Convex, Saddle and Developable Surfaces with No Smoothness Requirement
    3.1. Classes of Non-Smooth Surfaces and Metrics
    3.2. Questions of Approximation
    3.3. Results and Conjectures
    §4. Surfaces and Metrics of Bounded Curvature
    4.1. Manifolds of Bounded Curvature
    4.2. Surfaces of Bounded Extrinsic Curvature
    Chapter 2 Convex Surfaces
    §1. Weyl's Problem
    1.1. Statement of the Problem
    1.2. Historical Remarks
    1.3. Outline of One of the Proofs
    §2. The Intrinsic Geometry of Convex Surfaces. The Generalized Weyl Problem
    2.1. Manifolds of Non-Negative Curvat.ure in the Sense of Aleksandrov
    2.2. Solution of the Generalized Weyl Problem
    2.3. The Gluing Theorem
    §3. Smoothness of Convex Surfaces
    3.1. Smoothness of Convex Immersions
    3.2. The Advantage of Isothermal Coordinates
    3.3. Consequences of the Smoothness Theorems
    §4. Bendings of Convex Surfaces
    4.1. Basic Concepts
    4.2. Smoothness of Bendings
    4.3. The Existence of Bendings
    4.4. Connection Between Different Forms of Bendings
    §5. Unbendability of Closed Convex Surfaces
    5.1. Unique Determination
    5.2. Stability in Weyl's Problem
    5.3. Use of the Bending Field
    §6. Infinite Convex Surfaces
    6.1 Non-Compact Surfaces
    6.2. Description of Bendings
    §7. Convex Surfaces with Given Curvatures
    7.1. Hypersurfaces
    7.2. Minkowski's Problem
    7.3. Stability
    7.4. Curvature Functions and Analogues of the Minkowski Problem
    7.5. Connection with the Monge-Ampère Equations
    §8. Individual Questions of the Connection Between the Intrinsic and Extrinsic Geometry of Convex Surfaces
    8.1. Properties of Surfaces
    8.2. Properties of Curves
    8.3. The Spherical Image of a Shortest Curve
    8.4. The Possibility of Certain Singularities Vanishing Under Bendings
    Chapter 3 Saddle Surfaces
    §1. Efimov's Theorem and Conjectures Associated with It
    1.1. Sufficient Criteria for Non-Immersibility in E3
    1.2. Sufficient Criteria for Immersibility in E3
    1.3. Conjecture About a Saddle Immersion in En
    1.4. The Possibility of Non-Immersibility when the Manifold is Not Simply-Connected
    §2. On the Extrinsic Geometry of Saddle Surfaces
    2.1. The Variety of Saddle Surfaces
    2.2. Tapering Surfaces
    §3 Non-Regular Saddle Surfaces
    3.1. Definitions
    3.2. Intrinsic Geometry
    3.3. Problems of Immersibility
    3.4. Problems of Non-Immersibility
    Chapter 4 Surfaces of Bounded Extrinsic Curvature
    §1. Surfaces of Bounded Positive Extrinsic Curvature
    1.1. Extrinsic Curvatures of a Smooth Surface
    1.2. Extrinsic Curvatures of a General Surface
    1.3. Inequalities
    §2. The Role of the Mean Curvature
    2.1. The Mean Curvature of a Non-Smooth Surface
    2.2. Surfaces of Bounded Mean Curvature
    2.3. Mean Curvature as First Variation of the Area
    §3. C1-Smooth Surfaces of Bounded Extrinsic Curvature
    3.1. The Role of the Condition of Boundedness of the Extrinsic Curvature
    3.2. Normal C1-Smooth Surfaces
    3.3. The Main Results
    3.4. Gauss's Theorem
    3.5. C1,α-Smooth Surfaces
    §4. Polyhedra
    4.1. The Role of Polyhedra in the General Theor
    4.2. Polyhedral Metric and Polyhedral Surface
    4.3. Results and Conjectures
    §5. Appendix. Smoothness Classes
    Comments on the References
    References
    II. Surfaces of Negative Curvature
    Preface
    §1. Hilbert's Theorem
    1.1. Statement of the Problem
    1.2. Plan of the Proof of Hilbert's Theorem
    1.3. Connection with the Equations of Mathematical Physics
    1.4. Generalizations
    §2. Surfaces of Negative Curvature in E3. Examples. Intrinsic and Extrinsic Curvature. Hadamard's Problem
    2.1. Examples of Surfaces of Negative Curvature in E3, and Their Extrinsic and Intrinsic Geometry
    2.2. Some Remarks on a C1-Isometric Embedding of L2 in E3 According to Kuiper
    2.3. Hadamard's Conjecture
    2.4. Surfaces of Negative Intrinsic and Bounded Extrinsic Curvature in E3
    §3. Surfaces of the Form z=f(x,y); Plan of the Proof of Efimov's Theorem
    3.1. Some Results on Surfaces that Project One-to-one on the Plane E2
    3.2. A Theorem of Efimov and Heinz on the Extent of a One-to-one Projection onto the Plane of a Surface with Negative Curvature Separated from Zero
    3.3. Plan of the Proof of Theorem B
    §4. Surfaces with Slowly Varying Curvature. Immersion of Metrics of Negative Curvature in E3. The Influence of the Metric on the Regularity of a Surface
    4.1. Analytic Apparatus
    4.2. (h, △)-Metrics
    4.3. q-Metrics
    4.4. Immersion of Metrics of Negative Curvature in E3
    4.5. Study of the Boundary of a Surface
    4.6. Surfaces with Slowly Varying Curvature in a Riemannian Space
    4.7. Influence of the Metric on the Regularity of a Surface
    §5. On Surfaces with a Metric of Negative Curvature in Multidimensional Euclidean Spaces
    5.1. Bieberbach's Theorem
    5.2. Embedding and Immersion of Lp in EN
    5.3. Piecewise-Analytic Immersion of L2 in E4
    5.4. Some Results on Non-Immersibility in the Multidimensional Case
    5.5. On Closed Surfaces of Negative Curvature
    Commentary on the References
    References
    III. Local Theory of Bendings of Surfaces
    Preface
    §1. Definitions and Terminologies
    1.1. A Surface and Its Metric
    1.2. Isometric Surfaces and Isometric Immersions
    1.3. Bendings of Surfaces
    1.4. Infinitesimal Bendings of Surfaces
    1.5. Bendings of Surfaces and the Theory of Elastic Shells
    1.6. Areal Deformations
    §2. Statement of Problems
    §3. Connection Between Bendings and Infinitesimal Bendings of Surfaces
    3.1. General Equations of Infinitesimal Bendings of Arbitrary Order
    3.2. Transition from Infinitesimal Bendings of High Order to infinitesimal Bendings of Low Order
    3.3. Transition from Infinitesimal Bendings of Low Order to Infinitesimal Bendings of High Order
    3.4. Algebraic Properties of Fields of Infinitesimal Bendings of the lst Order
    §4. Bendings of Surfaces in the Class C1
    §5. Auxiliary Information: Classification and Integral Characteristics of Points of a Surface; Equations of Immersion and Bending
    5.1. Four Types of Points on a Surface
    5.2. Arithmetic Characteristics of a Regular Point of a Surface
    5.3. Stability and Instability of Arithmetic Characteristics of a Point of a Surface
    5.4. Equations of an Immersion and a Bending of a Surface
    §6. Bendings of Surfaces in a Neighbourhood of a Point of General Position
    6.1. Analytic Case
    6.2. Surfaces of Positive Curvature
    6.3. Surfaces of Negative Curvature
    6.4. Neighbourhood of a Parabolic Point
    §7. Bendability of Surfaces with a Flat Point
    7.1. Non-Applicable Isometric Surfaces
    7.2. On the Realization of Metrics by Surfaces with a Flat Point
    7.3. Non-Bendable Surfaces With a Flattening
    7.4. Bendable Surfaces with a Flattening
    7.5. Surfaces of Revolution with Flattening at a Pole
    §8. Infinitesimal Bendings of Surfaces "in the small"
    8.1. Equations of Infinitesimal Bendings
    8.2. Rigidity "in the small" of Analytic Surfaces
    8.3. Analytic Surfaces of Revolution with Flattening at a Pole
    8.4. Rigid and Non-Bendable "in the large" Surfaces of Revolution
    8.5. Non-Analytic Surfaces
    8.6. Infinitesimal Bendings of the 2nd Order
    8.7. Bendings of Troughs
    §9. Supplement. Bendings and Infinitesimal Bendings of Polyhedra
    9.1. Introduction
    9.2. Polyhedral Metrics and Their Isometric Immersions
    9.3. Bendings of Polyhedra. Configuration Spaces of Polyhedra
    9.4. Infinitesimal Bendings of Polyhedra and Their Connection with Bendings
    9.5. Uniquely Determined Polyhedra
    9.6. Non-Bendable Polyhedra
    9.7. Bendable Polyhedra
    9.8. Conjecture on the Invariance of the Volume of a Bendable Polyhedron
    §10. Concluding Remarks
    Comments on the References
    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