On the $\mathcalQ$ Curvature Tensor of a Generalized Sasakian-Space-Form


U. C. De, P. Majhi




The object of the present paper is to study $\xi$-$\mathcal{Q}$ flat, $\phi$-$\mathcal{Q}$ flat generalized Sasakian-space-forms. Besides these, we consider generalized Sasakian-space-forms satisfying $P(\xi,X)\cdot \mathcal{Q}=0$, $\mathcal{Q}(\xi,X)\cdot P=0$ and $\mathcal{Q}(\xi,X)\cdot \mathcal{Q}=0$. As a consequence we obtain several important results. Finally, illustrative examples are given.