Polyhedral Kähler manifolds

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

One Introduction to Kähler Manifolds

Polyhedral Kähler Manifolds

In this article we introduce the notion of Polyhedral Kähler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and classify the singularities of the metric. The singularities form a divisor and the residues of the flat connection on the complement of the divisor give us a syste...

Locally conformal Kähler manifolds with potential

A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold M̃ with the deck transform group acting conformally on M̃ . If M admits a holomorphic flow, acting on M̃ conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vaisman manifolds is stable under small deformations. We define a new class of LCK-manifolds, called LCK manifo...