Totally real submanifolds in a complex projective space (Q1283423)

Let \(P_n(\mathbb{C})\) be an \(n\)-dimensional complex projective space of constant holomorphic sectional curvature \(4\) and let \(M\) be an \(n\)-dimensional complete totally real minimal submanifold immersed in \(P_n(\mathbb{C})\). The author proves that if the scalar curvature of \(M\) is greater than \((3n+1)(n-2)/3\), then \(M\) is totally geodesic.