H-minimal Lagrangian fibrations in Kahler manifolds and minimal Lagrangian vanishing tori in Kahler-Einstein manifolds

Abstract

H-minimal Lagrangian submanifolds in general Kähler manifolds generalize special Lagrangian submanifolds in Calabi-Yau manifolds. In this paper we will use the deformation theory of H-minimal Lagrangian submanifolds in Kähler manifolds to construct minimal Lagrangian torus in certain Kähler-Einstein manifolds with negative first Chern class.

13 pages. We find that the "harmonic Lagrangian" we introduced is equivalent to "H-minimal Lagangian" studied by Oh 10 years ago. Revisions are made accordingly. Some results are simplified and rearranged