HARMONIC CURVATURE-LIKE TENSORS WITH SECOND BIANCHI IDENTITY ON KÄHLER MANIFOLDS

Abstract

We introduce the notion of curvature-like tensors on Kähler manifolds satisfying the second Bianchi equation. As examples, we mention concircular curvature tensor, projective curvature tensor, conformal curvature tensor and Bochner curvature tensor which are all closed curvature-like tensors. In particular, we show that all of them, except the concircular curvature tensor, are harmonic curvature-like tensors and give some conditions for them to be harmonic.