Conformal slant submersions in contact geometry

TL;DR

This paper introduces and explores conformal slant submersions from almost contact metric manifolds to Riemannian manifolds, generalizing several existing submersion concepts and analyzing their geometric properties.

Contribution

It defines conformal slant submersions, provides numerous examples, and investigates their geometric structures, including integrability, foliation geometry, and conditions for geodesic and harmonic maps.

Findings

Examples of conformal slant submersions are provided.

Conditions for integrability and totally geodesic foliations are established.

A decomposition theorem for the total space is proved.

Abstract

Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field $\xi$ is a vertical vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions and conformal anti-invariant submersions. More precisely, we mention lots of examples and obtain the geometries of the leaves of $\ker\pi_{*}$ and $(\ker\pi_{*})^\perp,$ including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the submersions. Finally, we consider a decomposition theorem on total space of the new submersion.