Curvature pinching for totally real submanifolds of a complex projective space

Abstract

Montiej Ros and Urbano [M3] showed a complete characterization of compact totally real minimal submanifold $M$ of $C{P}^n\left(c\right)$ with Ricci curvature $S$ of $M$ satisfying $S\ge 3(n-2)c/16$. The purpose of this paper is to answer Ogiue's conjecture which the above result remains true under the weaker condition of the scalar curvature $p$ of $M$ satisfying $p\ge 3n(n-2)c/16$.