(俄罗斯)波斯特尼科夫(M.M.Postnikov)[著] 本书特色

This book contains a systematic and comprehensive expositioof Lobachevskiageometry and the theory ofdiscrete groups ofmotions iEuclideaspace and Lobachevsky space. It is divided into two closely related parts： the first treats the geometry ofspaces ofconstant curvature and the second discrete groups of motions of these. The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry， Riemanniageometry and group theory. The result is a book which has no rivalithe literature.Part I contains the classificatioofmotions ispaces ofconstant curvature and non-traditional topics like the theory ofacute-angled polyhedra and methods for computing volumes of non-Euclideapolyhedra. Part II includes the theory of cristallographic， Fuchsian，and Kleiniagroups and aexpositioof Thurston's theory of deformations.The greater part of the book is accessible to first-year students imathematics. At the same time the book includes very recent results which will be ofinterest to researchers ithis field.

(俄罗斯)波斯特尼科夫(M.M.Postnikov)[著] 内容简介

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(俄罗斯)波斯特尼科夫(M.M.Postnikov)[著] 目录

Ⅰ．Geometry of Spaces of Constant Curvature
Preface
Chapter 1 Basic Structures
1 Definitioof Spaces of Constant Curvature
1．1 Lie Groups of Transformations
1．2 Groups of Motions of a RiemanniaManifold
1．3 Invariant RiemanniaMetrics oHomogeneous Spaces
1．4 Spaces of Constant Curvature
1．5 Three Spaces
1．6 Subspaces of the Space R
2 The ClassificatioTheorem
2．1 Statement of the Theorem
2．2 Reductioto Lie Algebras
2．3 The Symmetry
2．4 Structure of the Tangent Algebra of the Group of Motions
2．5 RiemanSpace
3 Subspaces and Convexity
3．1 Involutions
3．2 Planes
3．3 Half-Spaces and Convex Sets
3．4 Orthogonal Planes
4 Metric
4．1 General Properties
4．2 Formulae for Distance ithe Vector Model
4．3 Convexity of Distance
Chapter 2 Models of Lobachevskij Space
1 Projective Models
1．1 Homogeneous Domains
1．2 Projective ModelofLobachevskij Space
1．3 Projective EuclideaModelsThe KleiModel
1．4 "Affine" Subgroup of the Group of Automorphisms of a Quadric
1．5 RiemanniaMetric and Distance BetweePoints ithe Projective Model
2 Conformal Models
2．1ConformaISpace
2．2 Conformal Model of the Lobachevskij Space
2．3 Conformal EuclideaModels
2．4 Complex Structure of the Lobachevskij Plane
……
References

自然科学 数学 几何与拓扑

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