Abstract
We study the orbit space and totally geodesic orbits arising from isometric action of a compact and connected Lie group on a globally hyperbolic spacetime with non-negative curvature along timelike planes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. N. Bernal and M. Sanchez, Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes, Commun. Math. Phys., 257 (2005), 43–50.
G. B. Bredon, Introduction to Compact Transformation Groups, Academic Press (New York, London, 1972).
S. Kobayashi, Homogeneous Riemannian manifolds of negative curvature, Tohoku Math. J., 14 (1962), 413–415.
R. Mirzaie, On negatively curved G-manifolds of low cohomogeneity, Hokkaido Math. J., 38 (2009), 797–803.
R. Mirzaie, On Riemannian manifolds of constant negative curvature, J. Korean Math. Soc., 48 (2011), 23–21.
R. Mirzaie, Actions without non-trivial singular orbits on Riemannian manifolds of negative curvature, Acta Math. Hungar., 147 (2015), 172–178.
R. Mirzaie, On orbits of isometric ations on flat Riemannian amnifolds, Kyushu J. Math., 65(2011), 383–393.
B. O’Neill, Semi-Riemannian Geomerty with Applications to Relativity, Academic Press (New York, Berkeley, 1983).
F. Podesta and A. Spiro, Some topological propetrties of cohomogeneity one Riemannian manifolds with negative curvature, Ann. Global Anal. Geom., 14(1996), 69–79.
D. Szeghy, Isometric actions of compact conneted Lie groups on globally hyperbolic Lorentz manifolds, Publ. Math. Debrecen, 71 (2007), 229–243.
J. A. Wolf, Homogeneity and bounded isometries in manifolds of negative curvature, Illinois J. Math., 8 (1964), 14–18.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Karimi, H., Mirzaie, R. On globally hyperbolic G-manifolds with non-negative timelike curvature. Acta Math. Hungar. 170, 183–193 (2023). https://doi.org/10.1007/s10474-023-01336-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-023-01336-4