On totally real surfaces of the nearly Kähler 6-sphere (Q1111173)

In Proc. Am. Math. Soc. 99, 741-749 (1987; Zbl 0618.53046) the present authors have studied totally real 3-dimensional submanifolds of the nearly Kähler 6-sphere. This paper is devoted to the study of totally real surfaces of the nearly Kähler 6-sphere. The authors prove that if M is a minimal 2-dimensional totally real submanifold of \(S^ 6(1)\) and M is homeomorphic to a sphere, then M is totally geodesic. Using this fact, they show that if M is compact and has non-negative Gaussian curvature K, then either \(K=0\), or \(K=1\). Finally, the authors dicuss some examples.