2016/04/14 by Alma L. Albujer, Henrique F. de Lima, Albujer, Alma L. +5
Mathematics · #53A07 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C42 #Secondary 35P15 #math.DG #msc:35P15 #msc:53A07 #msc:53C42
paper · pdf · doi:10.48550/arxiv.1604.04117
11 pages
arxiv created 2016/04/14 · arxiv updated 2016/04/15
Our purpose in this paper is to apply some maximum principles in order to study the rigidity of complete spacelike hypersurfaces immersed in a spatially weighted generalized Robertson-Walker (GRW) spacetime, which is supposed to obey the so called strong null convergence condition. Under natural constraints on the weight function and on the f-mean curvature, we establish sufficient conditions to guarantee that such a hypersurface must be a slice of the ambient space. In this setting, we also obtain new Calabi-Bernstein type results concerning entire graphs in a spatially weighted GRW spacetime.