On Quasi-Conformally Recurrent Manifolds with Harmonic Quasi-Conformal Curvature Tensor

Abstract

Abstract. The main objective of the paper is to provide a full classification of quasiconformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.