on 1-index of unstable spacelike hypersurfaces in pseudo-euclidean spheres

In mathematical physics, the stable hypersurfaces of constant mean curvature in pseudo-euclidian spheres have been in- terested by many researchers on general relativity. as an extension, the notion of index of stability has been introduced for unstable ones. the stability index (as a rate of distance from being stable) is de ned in terms of the laplace operator δ as the trace of hes- sian tensor. in this paper, we study an extension of stability index (namely, 1-index) of hypersurfaces with constant scalar curvature in pseudo-euclidian sphere 𝑆^𝑛+1 1 . 1-index is de ned based on the cheng-yau operator 2 as a natural extension of δ.