Kyungpook Mathematical Journal 2011; 51(1): 109-124
Published online March 23, 2011
Copyright © Kyungpook Mathematical Journal.
On Quasi-Conformally Recurrent Manifolds with Harmonic Quasi-Conformal Curvature Tensor
Absos Ali Shaikh, Indranil Roy
Department of Mathematics, University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India
Received: March 23, 2011; Revised: March 23, 2011; Accepted: March 23, 2011
The main objective of the paper is to provide a full classification of quasi-conformally 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.
Keywords: recurrent, quasi-conformally recurrent, conformally recurrent, Ricci recurrent, quasi-conformal curvature tensor, harmonic quasi-conformal curvature tensor, quasi-conformally symmetric, scalar curvature