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

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

Supporting Institution

Amasya University

Project Number

FMB-BAP18-0335

Thanks

Thank you to Amasya University for their support

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