Integral formula of Maslov index and its applications

Abstract

Let L be a Lagrangian submanifold of a Kähler manifold (M, J, ω). In the present paper, we give the integral formula of the Maslov index of L. Using this, we investigate relations between symplectic topological conditions and the mean curvature vector of L when (M, J, ω) is a Kähler-Einstein manifold with nonzero Ricci curvature.