Metric <i>f</i>-Contact Manifolds Satisfying the (<i>κ</i>, <i>μ</i>)-Nullity Condition

Abstract

We prove that if the f-sectional curvature at any point of a ( 2 n + s ) -dimensional metric f-contact manifold satisfying the ( κ , μ ) nullity condition with n > 1 is independent of the f-section at the point, then it is constant on the manifold. Moreover, we also prove that a non-normal metric f-contact manifold satisfying the ( κ , μ ) nullity condition is of constant f-sectional curvature if and only if μ = κ + 1 and we give an explicit expression for the curvature tensor field in such a case. Finally, we present some examples.

Keywords

• metric <i>f</i>-contact manifold
• <i>f</i>-(<i>κ</i>,<i>μ</i>) manifold
• <i>f</i>-(<i>κ</i>,<i>μ</i>)-space form