Maximal and Willmore Null Hypersurfaces in Generalized Robertson-Walker Spacetimes

Authors : Cyriaque ATİNDOGBÉ, Hippolyte HOUNNON

Pages : 70-85

Doi:10.33401/fujma.670266

View : 25 | Download : 10

Publication Date : 2020-06-10

Article Type : Research Paper

Abstract :We establish after some technical results a characterization of maximal null hypersurfaces in terms of a constant mean curvature screen foliation insert ignore into journalissuearticles values(in the slices); induced by the Chen`s vector field. Thereafter, bounds are provided for both the squared norm of the insert ignore into journalissuearticles values(screen); shape operator for non totally geodesic maximal null hypersurfaces and the scalar curvature of the fiber. In terms of the scalar curvature of the fiber and the warping function, we establish necessary and sufficient conditions for Null Convergence Condition insert ignore into journalissuearticles values(NCC); to be satisfied in which case we prove that there are no non totally geodesic maximal null hypersurfaces. A generic example consisting of graphs of functions defined on the fiber is given to support our results. Finally, we provide lower bounds for the extrinsic scalar curvature and give a characterization result for Willmore null hypersurfaces in generalized Robertson-Walker spacetimes.
Keywords : Generalized Robertson Walker spacetimes, Maximal null hypersurface, Willmore null hypersurface