%0 Journal Article
%T On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Esmaeili, Behzad
%A Pashaie, Firooz
%A Haghighatdoost, Ghorbanali
%D 2021
%\ 12/01/2021
%V 18
%N 4
%P 97-111
%! On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres
%K Spacelike
%K Newton transformation
%K Lorentz-Minkowski space
%K 1-minimal hypersurface
%R 10.22130/scma.2021.541680.1009
%X In mathematical physics, the stable hypersurfaces of constant mean curvature in pseudo-Euclidian spheres have been interested 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 defined in terms of the Laplace operator $\Delta$ as the trace of Hessian tensor. In this paper, we study an extension of stability index(namely, 1-index) of hypersurfaces with constant scalar curvature in pseudo-Euclidian sphere $\S_1^{n+1}$. 1-index is defined based on the Cheng-Yau operator $\Box$ as a natural extension of $\Delta$.
%U https://scma.maragheh.ac.ir/article_248103_e470e8ed71d63e0d14235a8da8e7b331.pdf