Minimal submanifolds in certain types of kaehler product manifold

Abstract

Let $M$ be a real $l$-dimensional minimal submanifold with flat normal connection in a kaehler product manifold $\overline{M}^m\times \overline{M}^n$ where $\overline{M}^m$ and $\overline{M}^n$ are complex $m$-dimensional and complex $n$-dimensional kaehler manifolds with constant holomorphic sectional curvature $c_1$ and $c_2$ respectively. We give a formula for the Laplacian of the second fundamental form of $M$. Specially we discuss the F-anti invariant case. We also give some applications of this formula.