Compact conformally Kähler Einstein-Weyl manifolds

Abstract

We give a description of compact conformally Kähler Einstein-Weyl manifolds whose Ricci tensor is Hermitian. IntroductionIn this paper we shall investigate compact Einstein-Weyl structures (M, [g], D) on a complex manifold (M, J ), dimM ≥ 4, which are conformally Kähler and whose Ricci tensor ρ D is Hermitian, i.e., ρ D is J -invariant.We give a complete classification of compact Einstein-Weyl structures

Killing and conformal Killing tensors

“…Pairs of distributions with this property were studied in [21] by A. Naveira under the name of almost product structures of type D 1 . Note that Killing tensors with two eigenvalues were intensively studied by W. Jelonek in [15], [16], [17] and also by B. Coll et al in [4]. In particular W. Jelonek proves that a Killing tensor with constant eigenvalues satisfies our condition (26).…”