Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-13T01:42:38.801Z Has data issue: false hasContentIssue false
  • English
  • Français

Homothetic maps of distinguishing space-times

Published online by Cambridge University Press:  17 April 2009

Jin-Hwan Kim
Jin-Hwan Kim
Affiliation:
Department of Mathematics, College of Science, Yeungnam University, P.O. Box 713–749, Kyungsan, Korea
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that if (M, g) is a distinguishing space-time, then any distance homothetic map from (M, g) onto arbitrary space-time (M′, g′) is a homothetic map; in particular, every distance preserving map is an isometry.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 3 , December 1990 , pp. 483 - 486
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Beem, J.K., ‘Homothetic maps of the space-time distance function and differentiability’, Gen. Relativity Gravitation 9 (1978), 793–799.Google Scholar
[2]Beem, J.K. and Ehrlich, P.E., Global Lorentzian Geometry (Marcel Dekker, 1981).Google Scholar
[3]Malament, D.B., ‘The class of continuous timelike curves determine the topology of space-times’, J. Math. Phys. 18 (1977), 1399–1404.Google Scholar
[4]Vyas, U.D. and Akolia, G.M., ‘Chronal isomorphism’, Gen. Relativity Gravitation 16 (1984), 1045–1051.Google Scholar