Some flatness conditions on normal metric contact pairs

Abstract

In this paper, the geometry of normal metric contact pair manifolds 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 positive 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 manifold with a positive scalar curvature and, is a space of constant curvature.

Keywords

• contact pairs
• curvature conditions
• hermitian contact pair

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