- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 2
- Generic $\xi^{\perp}$-Riemannian Submersions
Generic $\xi^{\perp}$-Riemannian Submersions
Authors : Ramazan Sari
Pages : 390-403
Doi:10.15672/hujms.723602
View : 14 | Download : 4
Publication Date : 2022-04-01
Article Type : Research
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