On J-parallel totally real three-dimensional submanifolds of S⁶ (1)

Abstract

In this paper, we study totally real submanifolds of the nearly Kähler six-dimensional unit sphere. Since in this case also, parallel submanifolds are totally geodesic, we introduce a weaker condition, namely that for any tangent vector v〈 (∇ h) (v, v, v), J v 〉 = 0 . We obtain a complete classification of totally real three-dimensional submanifolds of S6 (1) satisfying the above condition. © 2009 Elsevier B.V. All rights reserved.