# An introduction to non-K\"ahler geometry: A chemical analysis of complex manifolds

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Daniele Angella
(Dipartimento di Matematica e Informatica "Ulisse Dini", Università di Firenze)

created by daniele on 18 Sep 2016

modified on 04 Oct 2016

5 oct 2016
-- 14:00

Universitatea din Bucuresti

**Abstract.**

Since 50s, *K\"ahler manifolds* have been attracting much attention as a special subclass of *complex manifolds*, that is, geometric objects locally modelled on open subsets of the complex Euclidean space.
In fact, they share many properties with *projective manifolds*, --- their algebraic counterpart. This is due to the very feature of K\"ahler manifolds: three different structures, --- *complex*, *symplectic*, *Riemannian*, --- closely intertwine to make *analytic methods* available.

*Non-K\"ahler Geometry* is the attempt to carry out a chemical analysis of these different structures, in order to understand their specific role, and to interpret methods and results into a wider context.
Moreover, the construction of non-K\"ahler manifolds also answers to the demand of theoretical physics models, *e.g.* in type II String Theory.

From this point of view, we will address some questions concerning cohomological and metric aspects in Complex Geometry.