Holomorphic foliations and transversal real sub manifolds in Kahler manifolds

This talk is based on the ongoing joint work with Hisashi Kasuya (Osaka University). In this talk I will explain a new construction of a pair of a real submanifold and a holomorphic foliation in a Kahler manifold equipped with a torus action. This construction provides non-invariant complex structures on compact Lie groups and a generalization of LVM theory.