Transverse Killing forms on a Kähler foliation (Q2890339)

The paper studies transverse conformal Killing forms on a Riemannian manifold. These forms are generalizations of transverse conformal Killing fields. In particular, a transverse conformal Killing 1-form (resp. transverse Killing 1-form) is the dual form of a transversal conformal Killing vector field (resp. transversal Killing vector field). The Killing forms and conformal Killing forms on a Riemannian manifold have been studied by many authors in recent decades. Recently, Jung and Richardson proved that on a Riemannian foliation with a non-positive curvature endomorphism, any transverse Killing forms are parallel. This paper proves similar results without the curvature condition. Namely, the authors prove that on a Kähler foliation of codimension \(q\) on a compact manifold, any transverse Killing \(r\)-form (\(2 \leq r \leq q\)) is parallel (Theorems 3.3. and 3.11).