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de Lima, Eudes L. ; de Lima, Henrique F. ; Lima, Eraldo A. Jr. ; Medeiros, Adriano A.
Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 58 (2017), issue 2, pp. 183-196
MSC: 53B30, 53C42, 53C50 | MR 3666940 | Zbl 06773713 | DOI: 10.14712/1213-7243.2015.204
Keywords:
Lorentzian Killing warped product; complete spacelike hypersurfaces; parabolic spacelike hypersurfaces; entire Killing graphs
Summary:
In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.
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