A NEW MEASURE FOR THE STABILITY OF HYPERSURFACES IN THE N- DIMENSIONAL EUCLIDEAN SPACE
Abd El - Megid, M. (1986). A NEW MEASURE FOR THE STABILITY OF HYPERSURFACES IN THE N- DIMENSIONAL EUCLIDEAN SPACE. EKB Journal Management System, 1(2nd Conference on Applied Mechanical Engineering.), 35-44. doi: 10.21608/amme.1986.52565
Mohamed Afwat Abd El - Megid. "A NEW MEASURE FOR THE STABILITY OF HYPERSURFACES IN THE N- DIMENSIONAL EUCLIDEAN SPACE". EKB Journal Management System, 1, 2nd Conference on Applied Mechanical Engineering., 1986, 35-44. doi: 10.21608/amme.1986.52565
Abd El - Megid, M. (1986). 'A NEW MEASURE FOR THE STABILITY OF HYPERSURFACES IN THE N- DIMENSIONAL EUCLIDEAN SPACE', EKB Journal Management System, 1(2nd Conference on Applied Mechanical Engineering.), pp. 35-44. doi: 10.21608/amme.1986.52565
Abd El - Megid, M. A NEW MEASURE FOR THE STABILITY OF HYPERSURFACES IN THE N- DIMENSIONAL EUCLIDEAN SPACE. EKB Journal Management System, 1986; 1(2nd Conference on Applied Mechanical Engineering.): 35-44. doi: 10.21608/amme.1986.52565

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

The International Conference on Applied Mechanics and Mechanical Engineering
Article 56, Volume 1, 2nd Conference on Applied Mechanical Engineering., May 1986, Pages 35-44    PDF (1.49 M)
Document Type: Original Article
DOI: 10.21608/amme.1986.52565
Author
Mohamed Afwat Abd El - Megid
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.

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