Title of article :
On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres
Author/Authors :
Esmaeili, Behzad Department of Mathematics - Islamic Azad University Karaj Branch, Karaj, Iran , Pashaie, Firooz Department of Mathematics - Faculty of Sciences - University of Maragheh, Maragheh, Iran , Haghighatdoost, Ghorbanali Department of Mathematics - Azarbaijan Shahid Madani University, Tabriz, Iran
Abstract :
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 Δ 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 §n+11. 1-index is defined based on the Cheng-Yau operator □ as a natural extension of Δ.
Keywords :
Spacelike , Newton transformation , Lorentz-Minkowski space , 1-minimal hypersurface
Journal title :
Sahand Communications in Mathematical Analysis
