Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

Alexey V. Shchepetilov (Autor)

Buch | Softcover

XVIII, 242 Seiten

2010 | 1. Softcover reprint of hardcover 1st ed. 2006
Springer Berlin (Verlag)
978-3-642-07127-0 (ISBN)

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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.

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.

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)

Erscheint lt. Verlag	22.10.2010
Reihe/Serie	Lecture Notes in Physics
Zusatzinfo	XVIII, 242 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	416 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Curvature • Differential Geometry • Hamiltonian functions • Integrable Systems • manifold • Potential • Riemannian spaces • two-body problem
ISBN-10	3-642-07127-9 / 3642071279
ISBN-13	978-3-642-07127-0 / 9783642071270
Zustand	Neuware