We prove that if the f-sectional curvature at any point of a $(2n+s)$ -dimensional metric f-contact manifold satisfying the $(\kappa ,\mu )$ 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 $(\kappa ,\mu )$ nullity condition is of constant f-sectional curvature if and only if $\mu =\kappa +1$ and we give an explicit expression for the curvature tensor field in such a case. Finally, we present some examples.

中文翻译：

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满足（κ，μ）-零条件的度量f-接触流形

我们证明如果f截面曲率在a的任何点 $（2ñ+s）$ 尺寸的f接触流形满足 $（\kappa ，\mu ）$ 具有的无效条件 $ñ>\mathrm{1个}$ 与点的f截面无关，则在流形上恒定。此外，我们还证明了一个非正常指标˚F -接触歧管满足 $（\kappa ，\mu ）$ 当且仅当以下情况时，无效条件具有恒定的f截面曲率： $\mu =\kappa +\mathrm{1个}$ 在这种情况下，我们给出了曲率张量场的显式表达式。最后，我们给出一些例子。