Transverse conformal Killing forms on Kähler foliations

Abstract

On a closed, connected Riemannian manifold with a Kähler foliation of codimension q = 2 m , any transverse Killing r ( ≥ 2 ) -form is parallel (Jung and Jung, 2012). In this paper, we study transverse conformal Killing forms on Kähler foliations. In fact, if the foliation is minimal, then for any transverse conformal Killing r -form ϕ ( 2 ≤ r ≤ q − 2 ) , J ϕ is parallel. Here J is defined in Section 4 .