Generalized complex and paracomplex structures on product manifolds

EDISON FERNÁNDEZ-CULMA; GODOY, YAMILE; MARCOS SALVAI

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS

REAL ACAD CIENCIAS EXACTAS FISICAS & NATURALES

Año: 2020 vol. 114

1578-7303

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.