Lagrangian Submersions from Normal Almost Contact Manifolds

Abstract

We study Lagrangian submersions from Sasakian and Kenmotsu manifolds onto Riemannian manifolds.
We prove that the horizontal distribution of a Lagrangian submersion
from a Sasakian manifold onto a Riemannian manifold admitting vertical Reeb vector field is
integrable, but the one admitting horizontal Reeb vector field is not.
We also show that the horizontal distribution of a such submersion is
integrable when the total manifold is Kenmotsu. Moreover, we give some applications of these results.