Generic $\xi^{\perp}$-Riemannian Submersions

Abstract

As a generalization of semi-invariant ξ ⊥ -Riemannian submersions, we introduce the generic ξ ⊥ -Riemannian submersions. We focus on the generic ξ ⊥ -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 ξ ⊥ -Riemannian submersion from Sasakian space forms are obtained and we prove that if the distributions, which define a generic ξ ⊥ -Riemannian submersion are totally geodesic, then they are Einstein.