Let be a pseudo‐Riemannian manifold of signature (n + 1, n). One defines on an almost cosymplectic para f‐structure and proves that a manifold endowed with such a structure is ξ‐Ricci flat and is foliated by minimal hypersurfaces normal to ξ, which are of Otsuki′s type. Further one considers on a 2(n − 1)‐dimensional involutive distribution P⊥ and a recurrent vector field . It is proved that the maximal integral manifold M⊥ of P⊥ has V as the mean curvature vector (up to 1/2(n − 1)). If the complimentary orthogonal distribution P of P⊥ is also involutive, then the whole manifold is foliate. Different other properties regarding the vector field are discussed.