Document Type : Research Paper


1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

2 Department of Mathematics, Faculty of Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.

3 Department of Mathematics, Azarbaijan Shahid Madani University, P.O.Box 53714-161, Tabriz, Iran.


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 $\Delta$.


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