Abstract
Applying generalized maximum principle and weak maximum principle, we obtain several uniqueness results for spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker (GRW) space-time under suitable geometric assumptions. Furthermore, we also study the special case when the ambient space is static and provide some results by using Bochner’s formula.
Highlights
In recent years, spacelike hypersurfaces in Lorentzian manifolds have been deeply studied from their mathematical interest, and from their importance in general relativity.there are many articles that study spacelike hypersurfaces in weighted warped product space-times
The weighted manifold Mf associated with a complete n-dimensional Riemannian manifold (Mn, g) and a smooth function f on Mn is the triple (Mn, g, dμ = e−fdM), where dM stands for the volume element of Mn
In this paper we study spacelike hypersurfaces in a weighted generalized Robertson-Walker (GRW) space-times
Summary
Spacelike hypersurfaces in Lorentzian manifolds have been deeply studied from their mathematical interest, and from their importance in general relativity. In [2], Wei and Wylie considered the complete n-dimensional weighted Riemannian manifold and proved mean curvature and volume comparison results on the assumption that the ∞-Bakry-Emery Ricci tensor is bounded from below and f or |∇f| is bounded. [4] obtained new Calabi-Bernstein’s type results related to complete spacelike hypersurfaces in a weighted GRW space-time. Some rigidity results of complete spacelike hypersurfaces immersed into a weighted static GRW space-time are given in [5].
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