On Lagrangian submersions

Abstract

In this paper, we study Riemannian, anti-invariant Riemannian and Lagrangian submersions. We prove that the horizontal distribution of a Lagrangian submersion from a Kahlerian manifold is integrable. We also give some applications of this result. Moreover, we investigate the effect of the submersion to the geometry of its total manifold and its fibers.