SOME FLATNESS CONDITIONS ON NORMAL METRIC CONTACT PAIRS

Abstract

In this paper, the geometry of normal metric contact pair mani- folds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and has pos- itive sectional curvature. It is also shown that a concircular flat normal metric contact pair manifold is an Einstein manifold. Finally, it is obtained that a quasi-conformally flat normal metric contact pair manifold is an Einstein man- ifold with a positive scalar curvature and, is a space of constant curvature.