Interpolation of geometric structures compatible with a pseudo Riemannian metric

EDISON ALBERTO FERNÁNDEZ-CULMA; YAMILE GODOY; MARCOS SALVAI

Córdoba

Jornada; Jornadas de Geometría; 2017

Generalized complex structures were introduced by N. Hitchin in 2003. In a smooth manifold theses structures interpolate between complex and symplectic structures. Given a pseudo Riemannian manifold $(M,g)$, we define four generalized geometric structures on $M$. Each of them interpolate between two geometric structures on $M$ compatible with $g$.We present some properties of the new structures, compute the typical fibers of their twistor bundles and give examples for $M$ a Lie group with a left invariant metric.