Vivana del Barco (UNICAMP, Brésil and Université Paris Sud) will speak in the geometry seminar on the 24th of April. The talk will take place in the Salle de Profs (9th floor, NO) at 13.30pm. Viviana’ title is Hermitian geometry of real flag manifolds and the abstract is below.
The aim of this talk is to present recent results about the Hermitian
geometry of real flag manifolds M=G/P.We will discuss results regarding the classification of those real flags
admitting almost complex structures which are invariant under the maximal
compact subgroup of the simple split Lie group G. In particular, it will
be shown that these manifolds are never K\”ahler, since they cannot carry
symplectic structures. Nevertheless,
other of the sixteen types of Hermitian structures with respect to
Gray-Hervella’s classification appear. For instance, invariant Hermitian
structures admitting metric connections with totally skew-symmetric
torsion can be given when G is type C; these structures can be induced to
the complex Stiefel manifold.The talk is based on works in collaboration with Ana Paula Cruz de Freitas
and Luiz San Martin, from Unicamp, Brazil.