Some Remarks on Bochner Curvature Tensors

This paper deals with the study of Kähler manifolds via Bochner curvature tensors. Similar study has been done by Kulkarni 4), 5), 6), where he has shown that many curvature preserving mappings between Rieamannian manifolds (or Kähler manifolds) reduce to conformal or isometric mappings. In the first section, we shall study K-curvature-like tensors on almost Hermitian manifolds which include Riemannian curvature tensors, Bochner curvature tensors, and so on. In the second section, we shall consider Bochner curvature tensors on Kähler manifolds. The characterizations of the Kähler manifold with vanishing Bochner curvature tensor have been obtained by many authors. We shall give some other conditions for vanishing Bochner curvature tensor in Theorem 2. In Theorem 3, we show an analogous result to Kulkarni for a HB-preserving mapping.