Kähler geometry

Abstract

[en] The main goal of this work is to provide an introductory dive into the subject of Complex Geometry by giving three different characterizations of Kähler manifolds and proving their equivalence. We define complex, Hermitian, Kähler and symplectic manifolds and we briefly study their properties. We present the Hodge conjecture and define the holonomy group. Finally, we present a brief glimpse into other types of spaces, namely Calabi-Yau and Hyperkähler manifolds.