On three dimensional quasi-Sasakian manifolds

Abstract

Let M be a 3-dimensional quasi-Sasakian manifold. Olszak [6] proved that M is conformally flat with constant scalar curvature and hence its structure function $\beta$ is constant. We have shown that in such M, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. A necessary and sufficient condition for such a manifold to be minimal has been obtained. Finally if such M satisfies $R(X,Y).S =0$, then, S has two different non-zero eigen values.