Skip to main content
SpringerLink
Log in
Book cover

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

  • Book
  • © 2006

Overview

Authors:
  1. Alexey V. Shchepetilov

    1. Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Physics (LNP, volume 707)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages I-XVII
    Download chapter PDF

  2. Two-Point Homogeneous Riemannian Spaces

    • Alexey V. Shchepetilov
    Pages 1-22

  3. Differential Operators on Smooth Manifolds

    • Alexey V. Shchepetilov
    Pages 23-49

  4. Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces

    • Alexey V. Shchepetilov
    Pages 51-86

  5. Hamiltonian Systems with Symmetry and Their Reduction

    • Alexey V. Shchepetilov
    Pages 87-111

  6. Two-Body Hamiltonian on Two-Point Homogeneous Spaces

    • Alexey V. Shchepetilov
    Pages 113-126

  7. Particle in a Central Field on Two-Point Homogeneous Spaces

    • Alexey V. Shchepetilov
    Pages 127-160

  8. Classical Two-Body Problem on Two-Point Homogeneous Riemannian Spaces

    • Alexey V. Shchepetilov
    Pages 161-190

  9. Quasi-Exactly Solvability of the Quantum Mechanical Two-Body Problem on Spheres

    • Alexey V. Shchepetilov
    Pages 191-217

  10. Back Matter

    Pages 219-256
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia

    Alexey V. Shchepetilov

Bibliographic Information

  • Book Title: Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

  • Authors: Alexey V. Shchepetilov

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/b11771456

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2006

  • Hardcover ISBN: 978-3-540-35384-3Published: 06 September 2006

  • Softcover ISBN: 978-3-642-07127-0Published: 22 October 2010

  • eBook ISBN: 978-3-540-35386-7Published: 04 September 2006

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: XVIII, 242

  • Topics: Mathematical Methods in Physics, Differential Geometry, Classical Mechanics

Publish with us

Policies and ethics

Back to top

Search

Navigation