Compact Submanifolds in a Euclidean Space~!2008-11-11~!2009-10-09~!2010-02-11~!
Sharief Deshmukh · The Open Mathematics Journal · 2010
In this paper we use bounds on the Ricci curvature of an n-dimensional compact submanifold M of the Euclidean space R n+p to obtain a characterization of a sphere (cf.Theorem 1).Also we obtain a lower bound on the integral of the square of the length of mean curvature vector field H of this submanifold and show that the lower bound is attended if and only if the submanifold is a sphere giving another characterization of a sphere (cf.Theorem 2).