Generalized complex and paracomplex structures on product manifolds
Fernández Culma, Edison Alberto; Godoy, Yamile Alejandra; Salvai, Marcos Luis; Generalized complex and paracomplex structures on product manifolds; Real Acad Ciencias Exactas Fisicas & Naturales; Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-matematicas; 114; 13-7-2020; 1-16
Fernández Culma, Edison Alberto
Godoy, Yamile Alejandra
Salvai, Marcos Luis
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.