Transverse conformal Killing forms on Kahler foliations

TL;DR

This paper investigates transverse conformal Killing forms on K"ahler foliations, showing that under minimality conditions, certain forms become parallel, extending previous results on transverse Killing forms.

Contribution

It extends the study of transverse Killing forms to conformal Killing forms on K"ahler foliations, demonstrating that specific forms are parallel when the foliation is minimal.

Findings

Transverse conformal Killing forms are parallel under minimality.

For certain degrees, the form Jφ is parallel.

Extends previous results on transverse Killing forms.

Abstract

On a closed, connected Riemannian manifold with a K\"ahler foliation of codimension $q=2m$, any transverse Killing $r\ (\geq 2)$-form is parallel (S. D. Jung and M. J. Jung [\ref{JJ2}], Bull. Korean Math. Soc. 49 (2012)). In this paper, we study transverse conformal Killing forms on K\"ahler foliations and prove that if the foliation is minimal, then for any transversal conformal Killing $r$-form $\phi$ $(2\leq r \leq q-2)$, $J\phi$ is parallel. Here $J$ is defined in Section 4.