Montiej Ros and Urbano [M3] showed a complete characterization of compact totally real minimal submanifold of with Ricci curvature of satisfying . 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 of satisfying .
Yoshio MATSUYAMA. "Curvature pinching for totally real submanifolds of a complex projective space." J. Math. Soc. Japan 52 (1) 51 - 64, January, 2000. https://doi.org/10.2969/jmsj/05210051