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.
Rezensionen / Stimmen
From the reviews:
"This book has eight chapters and a bibliography list containing 215 references. It is written in a clear and straightforward way that makes it useful even for nonspecialists in the field. . In particular, the book contains interesting discussions of applications of the Poincaré section method to some problems in constant curvature spaces. . The book is a valuable complete source for many-body problems on two-point homogeneous spaces." (Alexei Tsygvintsev, Mathematical Reviews, Issue 2008 f)
Reihe
Auflage
1st ed. Softcover of orig. ed. 2006
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 16 mm
Gewicht
ISBN-13
978-3-642-07127-0 (9783642071270)
DOI
Schweitzer Klassifikation
Two-Point Homogeneous Riemannian Spaces.- Differential Operators on Smooth Manifolds.- Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces.- Hamiltonian Systems with Symmetry and Their Reduction.- Two-Body Hamiltonian on Two-Point Homogeneous Spaces.- Particle in a Central Field on Two-Point Homogeneous Spaces.- Classical Two-Body Problem on Two-Point Homogeneous Riemannian Spaces.- Quasi-Exactly Solvability of the Quantum Mechanical Two-Body Problem on Spheres.
