Semi-invariant submanifolds of (g, F)-manifolds

We introduce (g,F)-manifolds and initiate a study of their semi-invariant submanifolds. These submanifolds are generalizations of CR-submanifolds of Kaehler manifolds. We obtain necessary and sufficient conditions for the integrability of distributions on a semi-invariant submanifold and study the geometry of foliations defined by these distributions. In particular, for a large class of (g,F)-manifolds we prove the existence of a natural foliation on their semi-invariant submanifolds.