The totally geodesic coisotropic submanifolds in Kahler manifolds

In this paper, we consider the coisotropic submanifolds in a Kahler manifold of nonnegative holomorphic curvature. We prove an intersection theorem for compact totally geodesic coisotropic submanifolds and discuss some topological obstructions for the existence of such submanifolds. Our results apply to Lagrangian submanifolds and real hypersurfaces since the class of coisotropic submanifolds includes them. As an application, we give a fixed-point theorem for compact Kahler manifolds with positive holomorphic curvature. Also, our results can be further extended to nearly Kahler manifolds.