On Decomposible Quasi-Conformally Recurrent Spaces

Abstract

The object of the present paper is to study decomposable quasi-conformally recurrent spaces and obtained a full classification of such a space. It is proved that in a quasi-conformally recurerent decomposable space both the decompositions are generalized recurrent and also Einstein. Again it is shown that if a Riemannian manifold is decomposable quasi-conformally recurerent, then either the recurrence vectors in both the decomposition spaces are gradient or the decomposition spaces are of constant curvature. The existence of a decomposable quasi-conformally recurrent space is ensured by a proper example.