On totally real minimal submanifolds in \(CP^n(c)\) (Q1277165)

The author proves the following result. Let \(M^n\) be a totally real minimal submanifold in a complex projective \(n\)-space \(\mathbb{C} P^n(c)\) which has at most two principal curvatures with respect to every normal direction. If \(M^n\) is not totally geodesic, then \(M^n\) is either a parallel submanifold with \(n\geq 4\) or an \(H\)-umbilical minimal surface in \(\mathbb{C} P^2(c)\) \((H\)-umbilical in the sense of \textit{B.-Y. Chen} [Isr. J. Math. 99, 69-108 (1997; Zbl 0884.53014)]). In the former case, if \(n\) is even (respectively, odd), then \(M^n\) is isotropic (respectively, \(M^n\) does not exist). Hence, \(M^n\) is Einsteinian and is locally congruent to one of the following: \(SU(3)\), \(n=8\); \(SU(6)/Sp(3)\), \(n=14\); or \(E_6/F_4\), \(n=26\).