A NEW MEASURE FOR THE STABILITY OF HYPERSURFACES IN THE N- DIMENSIONAL EUCLIDEAN SPACE

Document Type : Original Article

Author

Military Technical College, Kobry El - Kobba, Cairo.

Abstract

A new measure of stability on hypersurfaces in En is introduced. 
It is the integral
£ (f) = ∫M H1 Hn-2 dσ
where H1 is the ith mean curvature of the hypersurface M. The general conditions for the stability of M under normal deformations are found. The stability on M under II- infinitismal and III-infinitismal deformations and the stability of M under the normal deformations which admit the relation
δ II =1/2 (n-1) H1 δ I are also discussed.