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几何 2 常曲率空间 🔍
E.B.Vinberg著, E.B. Vinberg[编著, Nberg Vi, (俄) 温贝格, E. B, Ė. B Vinberg 北京:科学出版社, 2009, 2009
英语 [en] · 中文 [zh] · PDF · 9.2MB · 2009 · 📗 未知类型的图书 · 🚀/duxiu/zlibzh · Save
描述
This Book Contains A Systematic And Comprehensive Exposition Of Lobachevskian Geometry And The Theory Of Discrete Groups Of Motions In Euclidean Space And Lobachevsky Space. The Authors Give A Very Clear Account Of Their Subject Describing It From The Viewpoints Of Elementary Geometry, Riemannian Geometry And Group Theory. The Result Is A Book Which Has No Rival In The Literature. Part I Contains The Classification Of Motions In Spaces Of Constant Curvature And Non-traditional Topics Like The Theory Of Acute-angled Polyhedra And Methods For Computing Volumes Of Non-euclidean Polyhedra. Part Ii Includes The Theory Of Cristallographic, Fuchsian, And Kleinian Groups And An Exposition Of Thurston's Theory Of Deformations. The Greater Part Of The Book Is Accessible To First-year Students In Mathematics. At The Same Time The Book Includes Very Recent Results Which Will Be Of Interest To Researchers In This Field. I. Geometry Of Spaces Of Constant Curvature / D.k. Alekseevskij, E.b. Vinberg, A.s. Solodovnikov -- Ii. Discrete Groups Of Motions Of Spaces Of Constant Curvature / E.b. Vinberg, O.v. Shvartsman. (ed.) H.b. Vinberg. Translation Of: Geometrii︠a︡ Ii, Issued As V. 29 Of The Serial: Itogi Nauki I Tekhniki. Sovremennye Problemy Matermatiki. Fundamentalʹnye Napravlenii︠a︡. Includes Bibliographical References And Indexes.
备用文件名
duxiu/initial_release/《几何：Ⅱ：常曲率空间》_12709808.zip
备用文件名
zlibzh/no-category/E.B.Vinberg著, E.B. Vinberg[编著, Nberg Vi, (俄) 温贝格, E. B, Ė. B Vinberg/几何 2 常曲率空间_29468706.pdf
备选标题
几何. II, 常曲率空间. II, Spaces of constant curvature Ji he. Chang qu l| kong jian. Spaces of constant curvature
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Ethnocultural Perspectives on Disaster and Trauma (Encyclopaedia of Mathematical Sciences)
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Geometry: Volume 2: Spaces of Constant Curvature (Encyclopaedia of Mathematical Sciences)
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Geometry II: Spaces of Constant Curvature (Encyclopaedia of Mathematical Sciences, 29)
备选标题
Geometry. II, Spaces of constant curvature = 几何. II, 常曲率空间
备选标题
几何/II/常曲率空间/国外数学名著系列/Geometry
备选作者
R. V Gamkrelidze; Yu D Bugaro; V. A Zalgaller; E. B Vinberg; Yu G Reshetnyak; M. M Postnikov
备选作者
Ernest Borisovitch Vinberg; Viktor Minachin
备选作者
Ėrnest Borisovich Vinberg
备选作者
E.B. Vinberg, (ed.)
备用出版商
Springer Spektrum. in Springer-Verlag GmbH
备用出版商
Steinkopff. in Springer-Verlag GmbH
备用出版商
科学出版社 Ke xue chu ban she
备用出版商
Springer Berlin
备用出版商
Science Press
备用出版商
Copernicus
备用出版商
Telos
备用版本
Encyclopaedia of mathematical sciences ;, v. 29, Berlin, New York, Germany, 1993
备用版本
Guo wai shu xue ming zhu xi lie (xu yi), Di 1 ban, ying yin ban, Beijing, 2009
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Guo wai shu xue ming zhu xi lie ;v56, Ying yin ban, 北京 Beijing, 2009
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Springer Nature, Berlin, Heidelberg, 2013
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United States, United States of America
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China, People's Republic, China
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... -- Vol. 29, Unknown, 1993
备用版本
1 edition, June 11, 1993
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Germany, Germany
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August 1993
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2008
备用版本
2001
元数据中的注释
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元数据中的注释
Includes bibliographical references and indexes.
Translation of: Geometrii͡a︡ II, issued as v. 29 of the serial: Itogi nauki i tekhniki. Sovremennye problemy matermatiki. Fundamentalʹnye napravlenii͡a︡.
元数据中的注释
РГБ
元数据中的注释
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备用描述
Spaces of constant curvature, i.e. Euclidean space, the sphere, and Loba chevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to that used to create the geometry we learned at school. However, since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space, the original source of our geometric intuition. Euclidean geometry has for a long time been deeply rooted in the human mind. The same is true of spherical geometry, since a sphere can naturally be embedded into a Euclidean space. Lobachevskij geometry, which in the first fifty years after its discovery had been regarded only as a logically feasible by-product appearing in the investigation of the foundations of geometry, has even now, despite the fact that it has found its use in numerous applications, preserved a kind of exotic and even romantic element. This may probably be explained by the permanent cultural and historical impact which the proof of the independence of the Fifth Postulate had on human thought.
Erscheinungsdatum: 25.06.1993
备用描述
<p><P>This book contains a systematic and comprehensive exposition of Lobachevskian geometry and the theory of discrete groups of motions in Euclidean space and Lobachevsky space. The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry, Riemannian geometry and group theory. The result is a book which has no rival in the literature. Part I contains the classification of motions in spaces of constant curvature and non-traditional topics like the theory of acute-angled polyhedra and methods for computing volumes of non-Euclidean polyhedra. Part II includes the theory of cristallographic, Fuchsian, and Kleinian groups and an exposition of Thurston's theory of deformations. The greater part of the book is accessible to first-year students in mathematics. At the same time the book includes very recent results which will be of interest to researchers in this field.</p>
备用描述
This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. The author successfully combines the co-ordinate and invariant approaches to differential geometry, giving the reader tools for practical calculations as well as a theoretical understanding of the subject.
备用描述
A very clear account of the subject from the viewpoints of elementary geometry, Riemannian geometry and group theory – a book with no rival in the literature. Mostly accessible to first-year students in mathematics, the book also includes very recent results which will be of interest to researchers in this field.
备用描述
This chapter provides the definition of spaces of constant curvature and of their basic structures, and describes their place among homogeneous spaces on the one hand and Riemannian manifolds on the other.
开源日期
2024-06-13
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