Uniqueness Of Hypersurfaces In Generalized Robertson-Walker Spacetimes With Constant Higher Order Mean Curvature Quotients

This thesis is a research on the uniqueness problem of spacelike hypersurfaces with constant higher order mean curvature quotients in GRW spacetimes,where higher order mean curvature quotients are defined as H_k/H_l,0≤l<k≤n,with H_kand H_l being the higher order mean curvature with respect to corresponding orders.In the first part,we give some preliminary knowledge on semi-Riemannian geometry.Then,we introduce the generalized Robertson-Walker(GRW)spacetimes,the ambient space in which our hypersurfaces are immersed,as well as some concepts pertaining to spacelike hypersurfaces contained in GRW spacetimes.Finally,we give some computations which are required in the proof of our main results.In the second part,we give our main results about the uniqueness of spacelike hypersurfaces with constant higher order mean curvature quotients in GRW spacetimes,both in compact and in complete noncompact cases.