Hemi-slant $\xi ^{\perp }-$Riemannian submersions in contact geometry

Abstract

M. A. Akyol and R. Sar\i \ [On semi-slant $\xi^\perp$-Riemannian submersions, Mediterr. J. Math. (2017) 14: 234.] defined semi-slant $\xi^{\perp}-$Rie-mannian submersions from Sasakian manifolds onto Riemannian manifolds. As a generalization of the above notion and natural generalization of anti-invariant $\xi ^{\perp }-$Riemannian submersions, semi-invariant $\xi ^{\perp }-$Riemannian submersions and slant submersions,  we study hemi-slant $\xi ^{\perp }-$Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We obtain the geometry of foliations, give some examples and find necessary and sufficient condition for the base manifold to be a locally product manifold. Moreover, we  obtain some curvature relations from Sasakian space forms between the total space, the base space and the fibres.