# Conformal anti-invariant $\xi^\perp-$submersions

## TL;DR

This paper introduces conformal anti-invariant 11-submersions from almost contact metric manifolds to Riemannian manifolds, analyzing their geometric properties, conditions for being totally geodesic and harmonic, and associated product structures.

## Contribution

It generalizes anti-invariant 11-submersions to conformal cases and explores their geometric and structural properties.

## Key findings

- Conditions for conformal anti-invariant 11-submersions to be totally geodesic.
- Conditions for these submersions to be harmonic.
- Existence of certain product structures on the total space.

## Abstract

As a generalization of anti-invariant $\xi^\perp-$Riemannian submersions, we introduce conformal anti-invariant $\xi^\perp-$submersions from almost contact metric manifolds onto Riemannian manifolds. We investigate the geometry of foliations which are arisen from the definition of a conformal submersion and find necessary and sufficient conditions for a conformal anti-invariant $\xi^\perp-$submersion to be totally geodesic and harmonic, respectively. Moreover, we show that there are certain product structures on the total space of a conformal anti-invariant $\xi^\perp-$submersion.