A splitting result for real submanifolds of a Kahler manifold

Abstract

Let (Z, ω) be a connected Kähler manifold with an holomorphic action of the complex reductive Lie group U C , where U is a compact connected Lie group acting in a hamiltonian fashion. Let G be a closed compatible Lie group of U C and let M be a G-invariant connected submanifold ofThe vice-versa is also investigated. We also characterize G-invariant real submanifolds such that the norm square of the gradient map is constant. As an application, we prove a splitting result for real connected submanifolds of (Z, ω) generalizing a result proved in [7], see also [1,3].