Minimal submanifolds in certain types of kaehler product manifold

Xingda Liu; Bang Xiao

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arXiv · 1612.06500

Minimal submanifolds in certain types of kaehler product manifold

Xingda Liu·Bang Xiao

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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.

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Xingda Liu, Bang Xiao. 2016-12-20. Minimal submanifolds in certain types of kaehler product manifold. https://arxiv.org/abs/1612.06500

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