Geometry II

Spaces of Constant Curvature

Buch | Softcover

IX, 256 Seiten

2011 | 1. Softcover reprint of the original 1st ed. 1993
Springer Berlin (Verlag)
978-3-642-08086-9 (ISBN)

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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.

I. Geometry of Spaces of Constant Curvature.- II. Discrete Groups of Motions of Spaces of Constant Curvature.- Author Index.

Erscheint lt. Verlag	22.9.2011
Reihe/Serie	Encyclopaedia of Mathematical Sciences
Co-Autor	D.V. Alekseevskij, O.V. Shvartsman, A.S. Solodovnikov, E.B. Vinberg
Übersetzer	V. Minachin
Zusatzinfo	IX, 256 p. 10 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	416 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Analysis • Crystallographic groups • Diskrete Bewegungsgruppen • Fuchsian Groups • Fuchssche Gruppen • Hyperbolic Geometry • Hyperbolische Geometrie • Kristallographische Gruppen • Lobachevsky Space • Lobatschewskischer Raum • Räume konstanter Krümmung • reflection groups • Riemannian Geometry • Spaces of Constant Curvature • Volume
ISBN-10	3-642-08086-3 / 3642080863
ISBN-13	978-3-642-08086-9 / 9783642080869
Zustand	Neuware