Generalized complex and paracomplex structures on product manifolds

EDISON ALBERTO FERNÁNDEZ-CULMA; YAMILE GODOY; MARCOS SALVAI

Córdoba

Workshop; Workshop "Geometric Structures and Moduli Spaces"; 2022

FAMAF - UNC

On a product manifold (M, r), we consider four geometric structures compatible with r, e.g. hyper-paracomplex or bi-Lagrangian, and define distinguished generalized complex or paracomplex structures on M, which interpolate between some pairs of them. We study the twistor bundles whose smooth sections are these new structures, obtaining the typical fibers as homogeneous spaces of classical groups. Also, we give examples of product manifolds admitting some of these new structures.