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We prove that if the $f$-sectional curvature at any point $p$ of a$(2n+s)$-dimensional $f$-$(\kappa,\mu)$ manifold with $n>1$ is independent ofthe $f$-section at $p$, then it is constant on the manifold. Moreover, we alsoprove that an $f$-$(\kappa,\mu)$ manifold which is not an $S$-manifold is ofconstant $f$-sectional curvature if and only if $\mu=\kappa+1$ and we give anexplicit expression for the curvature tensor field. Finally, we present someexamples.

Metric $f$-contact manifolds satisfying the $(\kappa,\mu)$-nullity condition