Geometriae Dedicata

, Volume 27, Issue 3, pp 325–334

On totally real surfaces of the nearly Kaehler 6-sphere

  • F. Dillen
  • B. Opozda
  • L. Verstraelen
  • L. Vrancken
Article

DOI: 10.1007/BF00181497

Cite this article as:
Dillen, F., Opozda, B., Verstraelen, L. et al. Geom Dedicata (1988) 27: 325. doi:10.1007/BF00181497

Abstract

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.

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • F. Dillen
    • 1
  • B. Opozda
    • 2
  • L. Verstraelen
    • 1
  • L. Vrancken
    • 1
  1. 1.Department of MathematicsKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Department of MathematicsUniversity of CracówCracówPoland