Semi-invariant xi(perpendicular to)-Riemannian submersions from almost contact metric manifolds

Abstract

As a generalization of anti-invariant xi(perpendicular to)-Riemannian submersions, we introduce semiinvariant xi(perpendicular to)-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We give examples, investigating the geometry of foliations which arise from the definition of a Riemannian submersion and proving a necessary and sufficient condition for a semi-invariant xi(perpendicular to)-Riemannian submersion to be totally geodesic. Moreover, we study semi-invariant xi(perpendicular to)-Riemannian submersions with totally umbilical fibers.