Pseudo-holomorphic curves in nearly Kahler manifolds

We study pseudo-holomorphic curves in general nearly Kahler manifolds. For that purpose, we first introduce the fundamental equations of submanifold geometry in terms of the characteristic connection of the nearly Kahler structure. Then we classify pseudo-holomorphic curves with parallel second fundamental form in Chern-flat nearly Kahler manifolds. Moreover, we give a new Simons type identity. As an application of this identity, we show that the closed pseudo-holomorphic curves in Chern-flat nearly Kahler manifolds with a second fundamental form of controlled growth are totally geodesic. (C) 2014 Elsevier B.V. All rights reserved.