Totally complex submanifolds of the Cayley projective plane

Abstract

Let $K$ be the sectional curvature of a compact submanifold $M$ of the Cayley projective plane $CaP^{2}$. In this paper, we prove that the compact totally complex submanifold $M$ of complex dimension 2 in $CaP^{2}$ satisfying $K \gt (1/8)$ is totally geodesic and $M=CP^{2}$.