# Anti-invariant Riemannian submersions from locally conformal Kaehler manifolds

## TL;DR

This paper extends the concept of anti-invariant Riemannian submersions to locally conformal Kaehler manifolds, exploring their geometric properties and decomposition theorems.

## Contribution

It introduces the notion of anti-invariant and Lagrangian Riemannian submersions in the context of locally conformal Kaehler manifolds, expanding prior work on Hermitian manifolds.

## Key findings

- Discusses the geometry of foliations in these submersions
- Provides decomposition theorems for the total manifold
- Extends the theory to a broader class of manifolds

## Abstract

B. Sahin [9] introduced the notion of anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In the present paper we extend the notion of anti-invariant and Lagrangian Riemannian submersions (a special anti-invariant Riemannian submersion) to the case of locally conformal Kaehler manifolds. We discuss the geometry of foliation and obtain some decomposition theorems for the total manifold of such submersions.