Rigidity of complete spacelike hypersurfaces in spatially weighted generalized Robertson-Walker spacetimes

详细信息    查看全文

• 作者：Alma L. Albujer^a ; ^{alma.albujer@uco.es} ; Henrique F. de Lima^b ; ^{henrique@mat.ufcg.edu.br} ; Arlandson M. Oliveira^b ; ^{arlandsonm@gmail.com} ; Marco Antonio L. Velá ; squez^b ; ^{marco.velasquez@pq.cnpq.br}
• 关键词：primary ; 53C42 ; 53A07 ; secondary ; 35P15
• 刊名：Differential Geometry and its Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：50
• 期：Complete
• 页码：140-154
• 全文大小：416 K
• 卷排序：50

文摘

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 spacetime. In this setting, we also obtain new Calabi–Bernstein type results concerning entire graphs in a spatially weighted GRW spacetime.