Abstract.
Let M be a compact oriented minimal hypersurface of the unit ndimensional
sphere Sn. In this paper we will point out that if the Ricci curvature of M is
constant, then, we have that either Ric t^ 1 and M is isometric to an equator
or, n is odd, Ric t^ n-3n-2 and M is isometric to S n-12 ( p2 2 ) * S n-12 (
p2 2 ).Next, we will prove that there exists a positive number s^(n) such that
if the Ricci curvature of a minimal hypersurface immersed by first
eigenfunctions M satisfies that n-3n-2 - s^(n) <= Ric <= n-3n-2 + s^(n) and
the average of the scalar curvature is n-3n-2 , then, the ricci curvature of M
must be constant and therefore M must be isometric to S n-12 ( p2 2 ) * S n-12
( p2 2 ).
