Semi-invariant Submanifolds in Metric Geometry of Endomorphisms

Attempts have been made to introduce generalization of structured manifolds as the most general Riemannian metric g associated with an endomorphism F and initiate a study of their semi-invariant submanifolds. These submanifolds are generalizations of CR submanifolds of almost complex geometry and semi-invariant submanifolds of several interesting geometries (almost product, almost contact and others). Characterization of the integrability of both invariant and anti-invariant distribution are done; the special case when F is covariant constant with respect to g.