ENGLISH

Geometry II: Spaces of Constant Curvature

By D. V. Alekseevskij , E. B. Vinberg , A. S. Solodovnikov (auth.) , E. B. Vinberg (eds.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1993
ISBN
9780387520001, 0387520007
DOI
10.1007/978-3-662-02901-5
LCC
QA649 .G46513 1993
Open Library ID
OL1726939M
Language
english
Format
DJVU
Filesize
2 MB (1815823 bytes)
Series
Encyclopaedia of Mathematical Sciences 29
Edition
1
Pages
256\260
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Geometry; Analysis; Topological GroupsLie Groups

Description

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.

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