Metric $f$-contact manifolds satisfying the $(κ,μ)$-nullity condition

Abstract

We prove that if the f -sectional curvature at any point p of a (2n + s)-dimensional f -(κ, µ) manifold with n > 1 is independent of the f -section at p, then it is constant on the manifold. Moreover, we also prove that an f -(κ, µ) manifold which is not an S-manifold is of constant f -sectional curvature if and only if µ = κ + 1 and we give an explicit expression for the curvature tensor field. Finally, we present some examples.