General Relativity and Gravitation

, Volume 14, Issue 12, pp 1095–1105 | Cite as

Conformal hyperbolicity of Lorentzian warped products

  • Michael J. Markowitz
Research Articles


A space-timeM is said to be conformally hyperbolic if the intrinsic conformal Lorentz pseudodistanced M is a true distance. In this paper we first derive criteria which insure the conformal hyperbolicity of certain space-times which are generalizations of the Robertson-Walker spaces. Thend M is determined explicitly for Einstein-de Sitter space, and important cosmological model.


Differential Geometry Cosmological Model Warped Product True Distance Lorentzian Warped Product 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beem, J. K., Ehrlich, P. E., and Powell, T. G. (1979). Lorentzian warped product manifolds and geodesic completeness, preprint.Google Scholar
  2. 2.
    Beam, J. K., Ehrlich, P. E., and Powell, T. G. (to appear) Warped Product Manifolds in Relativity. Greek Einstein Centenary Symposium.Google Scholar
  3. 3.
    Hawking, S. W., and Ellis, G. F. R. (1973). The large scale structure of space-time, Cambridge University Press, Cambridge.Google Scholar
  4. 4.
    Kobayashi, S. (1970).Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York.Google Scholar
  5. 5.
    Kobayashi, S. (1978). Projective structures of hyperbolic type, inMinimal Submanifolds and Geodesics, Kaigai Publications, Tokyo.Google Scholar
  6. 6.
    Markowitz, M. (1981). An intrinsic conformal Lorentz pseudodistance,Math. Proc. Cambridge Philos. Soc.,89, 359–371.Google Scholar
  7. 7.
    Nomizu, K. (1980). Poincaré-Lorentz geometry on the upper half-plane, preprint.Google Scholar
  8. 8.
    Sachs, R. K., and Wu, H.-H. (1977).General Relativity for Mathematicians. Graduate Texts in Mathematics #48, Springer-Verlag, New York.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Michael J. Markowitz
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicago

Personalised recommendations