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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. document.getElementById('cloaked6348c90e73870cf79878ebdd5fc144').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyed6348c90e73870cf79878ebdd5fc144 = 'y&#97;m&#105;l&#101;.g&#111;d&#111;y' + '&#64;'; addyed6348c90e73870cf79878ebdd5fc144 = addyed6348c90e73870cf79878ebdd5fc144 + '&#117;nc' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r'; var addy_texted6348c90e73870cf79878ebdd5fc144 = 'y&#97;m&#105;l&#101;.g&#111;d&#111;y' + '&#64;' + '&#117;nc' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r';document.getElementById('cloaked6348c90e73870cf79878ebdd5fc144').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyed6348c90e73870cf79878ebdd5fc144 + '\'>'+addy_texted6348c90e73870cf79878ebdd5fc144+'<\/a>';

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).