University of MaraghehSahand Communications in Mathematical Analysis2322-580718420211201On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres9711124810310.22130/scma.2021.541680.1009ENBehzadEsmaeiliDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.FiroozPashaieDepartment of Mathematics, Faculty of Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh,
Iran.0000-0002-3020-7649GhorbanaliHaghighatdoostDepartment of Mathematics, Azarbaijan Shahid Madani
University, P.O.Box 53714-161, Tabriz, Iran.Journal Article20211027In 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<br />(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 $\Delta$.https://scma.maragheh.ac.ir/article_248103_e470e8ed71d63e0d14235a8da8e7b331.pdf