On totally real surfaces of the nearly Kaehler 6-sphere
- Cite this article as:
- Dillen, F., Opozda, B., Verstraelen, L. et al. Geom Dedicata (1988) 27: 325. doi:10.1007/BF00181497
Let M be a minimal totally real surface of the nearly Kaehler 6-sphere. We prove that if M is homeomorphic to a sphere, then M is totally geodesic. Consequently, if M is compact and has non-negative Gaussian curvature K, then eithe K=0 or K=1. Finally, we derive from these results that if M has constant Gaussian curvature K, then either K=0 or K=1.