Abelian hypercomplex manifolds and related structures

M.L. BARBERIS

Pisa, Italia

Workshop; Differential Geometry and Topology; 2004

Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore

This talk considers the construction of special geometric structures using solvable Lie groups. Starting with a canonical structure on euclidean space, we translate it by using different Lie groups acting simply transitively, so that one can work directly at the Lie algebra level.  We concentrate on the construction of geometric structures related to a particular class of invariant complex structures on Lie groups, namely the abelian ones. After an introduction surveying relevant results, we shall present applications related to weak HKT structures and compact hypercomplex non-hyperkähler nilmanifolds with holonomy in SL(n,H).