Comparison results for the volume of geodesic celestial spheres in Lorentzian manifolds

Volume comparison results are obtained for the volume of geodesic celestial spheres in Lorentzian manifolds and the corresponding objects in Lorentzian space forms. Also, as a rigidity result it is shown that the volume of geodesic celestial spheres is independent of the instantaneous observer if an...

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Bibliographic Details
Published in:Differential geometry and its applications 2005-07, Vol.23 (1), p.1-16
Main Authors: Díaz-Ramos, J. Carlos, García-Río, Eduardo, Hervella, Luis M.
Format: Article
Language:English
Subjects:
Jacobi fields
Scalar curvature invariants
Volume comparison
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Summary:Volume comparison results are obtained for the volume of geodesic celestial spheres in Lorentzian manifolds and the corresponding objects in Lorentzian space forms. Also, as a rigidity result it is shown that the volume of geodesic celestial spheres is independent of the instantaneous observer if and only if the spacetime has constant curvature.
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2005.03.001