Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

Shchepetilov, Alexey V.

Mathematics develops both due to demands of other sciences and due to its internal logic. The latter fact explains the attention of mathematicians to many problems, which are in close connection with basic mathematical notions, even if these problems have no direct practical applications. It is well known that the space of constant curvature is one of the basic geometry notion [208], which induced the wide ?eld for investigations. As a result there were found numerous connections of constant curvature spaces with other branches of mathematics, for example, with integrable partial dif- 1 ferential equations [36, 153, 189] and with integrable Hamiltonian systems [141]. Geodesic ?ows on compact surfaces of a constant negative curvature (with the genus 2) generate many test examples for ergodic theory (see also 3 [183] and the bibliography therein). The hyperbolic space H (R) is the space of velocities in special relativity (see Sect. 7.4.1) and also arises as space-like sections in some models of general relativity.

Details

Published by: Springer

Publication Date: 2006-09-06

Format: Hardcover

ISBN-13: 9783540353843

DOI: 10.1007/b11771456

Dimensions: 235.0cm x155.0cm

Pages: 242.0