Generic ??-Riemannian submersions

Abstract

As a generalization of semi-invariant xi(perpendicular to)-Riemannian submersions, we introduce the generic xi(perpendicular to)- Riemannian submersions. We focus on the generic xi(perpendicular to)-Riemannian submersions for the Sasakian manifolds with examples and investigate the geometry of foliations. Also, necessary and sufficient conditions for the base manifold to be a local product manifold are obtained and new conditions for totally geodesicity are established. Furthermore, curvature properties of distributions for a generic xi(perpendicular to)- Riemannian submersion from Sasakian space forms are obtained and we prove that if the distributions, which define a generic xi(perpendicular to)-Riemannian submersion are totally geodesic, then they are Einstein.