Generalized complex and paracomplex structures on product manifolds

EDISON ALBERTO FERNÁNDEZ-CULMA; YAMILE GODOY; MARCOS SALVAI

Congreso; Mathematical Congress of the Americas 2021; 2021

In 2003 Hitchin introduced generalized complex structures. They can be thought of as geometric structures on a smooth manifold interpolating between complex and symplectic structures, since these ones are particular extremal cases.Given a product manifold $(M, r)$ we define generalized geometric structures on $M$ which interpolate between two geometric structures compatible with $r$. 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 Lie groups with a left invariant product structure which admit some of these new structures.