Transverse conformal Killing forms on Kahler foliations

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.