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

Authors : Ramazan SARI

Pages : 390-403

Doi:10.15672/hujms.723602

View : 20 | Download : 5

Publication Date : 2022-04-01

Article Type : Research Paper

Abstract :As a generalization of semi-invariant $\xi ^{\perp }$-Riemannian submersions, we introduce the generic $\xi ^{\perp }$- Riemannian submersions. We focus on the generic $\xi ^{\perp }$-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 $\xi ^{\perp }$-Riemannian submersion from Sasakian space forms are obtained and we prove that if the distributions, which define a generic $\xi ^{\perp }$-Riemannian submersion are totally geodesic, then they are Einstein.
Keywords : Riemannian submersion, Sasakian manifolds, second fundamental form of a map, Einstein manifold