Introduction to complex geometry and Calabi-Yau manifolds motivated by physics

Abstract

[en] In this work, we give an introduction to complex geometry and Calabi-Yau manifolds. We begin by recalling the necessary background of differential geometry, as well as defining the de Rahm cohomology and the Ricci curvature. Then we turn to complex geometry, giving some precise examples, extending differential forms to the complex case and defining Dolbeault cohomology, Chern classes and holonomy. We then focus on Kähler manifolds, which are the previous steps to define Calabi-Yau manifolds, whose properties will be briefly studied. We close the work with a few ideas of a basic string theory model.