On Lagrangian submersions

TL;DR

This paper investigates properties of Lagrangian submersions from Kaehlerian manifolds, proving the integrability of the horizontal distribution and exploring their geometric implications.

Contribution

It establishes the integrability of the horizontal distribution in Lagrangian submersions from Kaehlerian manifolds and examines their geometric effects.

Findings

Horizontal distribution of Lagrangian submersion is integrable

Provides applications of the integrability result

Analyzes the impact on total manifold and fibers

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 Kaehlerian 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.