Almost hermitian structures on real flag manifolds

Jeudi 21 juin 2018 14:00-15:00 - Viviana del Barco - Orsay

Résumé : Real flag manifolds are submanifolds of complex flags ; the latter ones have been thoroughly studied and they admit complex, symplectic, Hermitian and even Kahler structures. It is natural then to ask about the possibility of having these structures on real flags. We show that, contrary to the complex case, these are never symplectic and therefore not Kahler. Nevertheless integrable complex structures can be found in type C : some specific manifolds of flags of isotropic subspaces of R^2n with respect to a symplectic structure carry complex structures. On these
particular cases we see where the pairs of invariant Riemannian metric-almost complex structures fit in the classification of Gray-Hervella of almost Hermitian structures.
The talk is based on (on-going) works in collaboration with Ana Paula Cruz de Freitas and Luiz San Martin, from UNICAMP, Brazil.

Lieu : salle 2L8 (IMO, bâtiment 307)

Notes de dernières minutes : Café culturel assuré à 13h par Andrei Moroianu.

Almost hermitian structures on real flag manifolds  Version PDF