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Session S23 - Group actions in Differential Geometry

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Generalized complex and paracomplex structures on product manifolds

Yamile Godoy

CIEM - FAMAF (Conicet - Universidad Nacional de Córdoba), Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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.

-E. A. Fernández-Culma, Y. Godoy, M. Salvai, Generalized complex and paracomplex structures on product manifolds. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114, No. 3, (2020) Paper No. 154.

Joint work with Edison Fernández-Culma (CIEM - FAMAF, Argentina) and Marcos Salvai (CIEM - FAMAF, Argentina).

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