INTEGRABILITY OF F-STRUCTURES ON GENERALIZED FLAG MANIFOLDS

Abstract. Here we consider a generalized flag manifold F = U/K, and a differential structure F which satisfy F3 +F = 0; these structures are called f-structures. Such structure F determines in the tangent bundle of F some ad(K)−invariant distributions. Since flag manifolds are homogeneous reduc-tive spaces, they certainly have combinatorial properties that allow us to make some easy calculations about integrability conditions for F itself and the distributions that it determines on F. An special case corresponds to the case U = U(n), the unitary group, this is the geometrical classical flag manifold and in fact tools coming from graph theory are very useful. 1