Event description
Abstract: Let M be a complex manifold of complex dimension n. A p-Kähler structure on M is a real, closed, transverse, (p,p)-form. In these talks, we will study some aspects of p-Kähler geometry. In particular, we will discuss the conjecture, stated by L. Alessandrini and G. Bassanelli, that a p-Kähler manifold is also a (p+1)-Kähler manifold. We will construct examples of nilmanifolds admitting p-Kähler structures and we will provide a necessary condition for the existence of smooth curves of p-Kähler structures, starting from a fixed p-Kähler structure, along a differentiable family of complex manifolds. Finally, we will investigate some cohomological consequences associated with the existence of a p-Kähler structure.