Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Lima, Jr., Adriano A. Medeiros
Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product

Abstract: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.

Keywords: Lorentzian Killing warped product; complete spacelike hypersurfaces; parabolic spacelike hypersurfaces; entire Killing graphs

DOI: DOI 10.14712/1213-7243.2015.204
AMS Subject Classification: 53C42 53B30 53C50