A dimensional restriction for a class of contact manifolds

In this work we consider a class of contact manifolds $(M,η)$ with an associated almost contact metric structure $(ϕ, ξ, η,g)$. This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class $C_9\oplus C_{10}$ defined by Chinea and Gonzalez. All manifolds in the class considered turn out to have dimension $4n+1$. Under the assumption that the sectional curvature of the horizontal $2$-planes is constant at one point, we obtain that these manifolds must have dimension $5$.

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