Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds

Abstract

The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved the nonexistence of (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that the characteristic vector field $\xi $ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field $\xi $ is a horizontal vector field and an anti-invariant horizontally conformal submersion such that $\xi $ is a vertical vector field.