Advertisement

Theoretical and Mathematical Physics

, Volume 103, Issue 2, pp 543–549 | Cite as

Dynamical systems on a Riemannian manifold that admit normal shift

  • A. Yu. Boldin
  • V. V. Dmitrieva
  • S. S. Safin
  • R. A. Sharipov
Article
  • 36 Downloads

Abstract

Newtonian dynamical systems that admit normal shift on an arbitrary Riemannian manifold are considered. The determining equations for these systems, which constitute the condition of weak normality, are derived. The extension of the algebra of tensor fields to manifolds is considered.

Keywords

Manifold Dynamical System Riemannian Manifold Tensor Field Determine Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Yu. Boldin and R. A. Sharipov,Teor. Mat. Fiz.,97, 386 (1993).Google Scholar
  2. 2.
    A. Yu. Boldin and R. A. Sharipov, “Dynamical systems that admit normal shift,” Preprint 0001-M [in Russian], Bashkir State University, Ufa (1993).Google Scholar
  3. 3.
    A. Yu. Boldin and R. A. Sharipov,Teor. Mat. Fiz.,100, 264 (1994).Google Scholar
  4. 4.
    L. Bianchi,Ann. Mat.,18, 185 (1911).Google Scholar
  5. 5.
    K. Tenenblat,Bol. Soc. Bras. Math.,18, 67 (1985).Google Scholar
  6. 6.
    R. A. Sharipov,Teor. Mat. Fiz.,101, 85 (1994).Google Scholar
  7. 7.
    S. Kobayashi and K. Nomizu,Foundations of Differential Geometry, Vols. 1 and 2, Interscience, New York (1963).Google Scholar
  8. 8.
    R. A. Sharipov,Usp. Mat. Nauk,49, 105 (1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. Yu. Boldin
  • V. V. Dmitrieva
  • S. S. Safin
  • R. A. Sharipov

There are no affiliations available

Personalised recommendations