Journal of the
Korean Mathematical Society JKMS

Let $S$ be the Ricci curvature of an $n$-dimensional compact minimal totally real submanifold $M$ of a quaternion projective space $HP^n(c)$ of quaternion sectional curvature $c$. We proved that if $S\le \frac{3(n-2)}{16}c$, then either $S\equiv \frac{n-1}4 c$ (i.e. $M$ is totally geodesic or $S\equiv \frac{3(n-2)}{16} c$. All compact minimal totally real submanifolds of $HP^n(c)$ satisfy in $S\equiv \frac{3(n-2)}{16} c$ are determined.

Keywords: quaternion projective space, totally real, minimal, Ricci curvature

MSC numbers: 53C40, 53C42