Biharmonic submanifolds of Kaehler product manifolds

Abstract

In this paper, the authors have established the necessary and sufficient conditions for the submanifolds of Kaehler product manifolds to be biharmonic. Moreover, the magnitude of scalar curvature for the hypersurfaces in a product of two unit spheres has been derived. Also, for the same product, the magnitude of the mean curvature vector for Lagrangian submanifolds has been estimated. Finally, the non-existence condition for totally complex Lagrangian submanifolds in a product of unit sphere and a hyperbolic space has been proved.

Keywords

• biharmonic submanifolds
• kaehler product manifolds
• totally real submanifolds
• lagrangian submanifolds
• mean curvature