Polyhedral Kähler Manifolds

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

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.

Automorphisms and the Kähler Cone of Certain Calabi-yau Manifolds

and let f = π1 · p = π2 · p2 : X → P . Schoen [S] has shown that if the surfaces are sufficiently general, then X is a smooth Calabi-Yau manifold. Let K(X) be the closure of the Kähler cone of X . By construction K(X) has infinitely many edges. Here we show that there is a fundamental domain which is a (finite) rational polyhedral cone, for the induced action of Aut(X) on K(X). Our work was ins...

A Theorem of Tits Type for Compact Kähler Manifolds

We prove a theorem of Tits type for compact Kähler manifolds, which has been conjectured in the paper [9].

Cohomologically Kähler Manifolds with No Kähler Metrics

We show some examples of compact symplectic solvmanifolds, of dimension greater than four, which are cohomologically Kähler and do not admit Kähler metric since their fundamental groups cannot be the fundamental group of any compact Kähler manifold. Some of the examples that we study were considered by Benson and Gordon (1990). However, whether such manifolds have Kähler metrics was an open que...

On Multiplier Hermitian Structures on Compact Kähler Manifolds