Kenmotsu manifold carrying a skew symmetric Killing vector field M.FerraraandC.German`a Abstract In the present note we use a Kenmotsu manifold M(Φ, Ω,η,ξ,f ), (in the sense of Z.Olszak and R.Ro¸ sca [3]) carrying a skew symmetric Killing vector field X (in the sense of R.Rosca [7], to show that X, under certain conditions, defines a relative conformal transformation of a structure 2-form Ω. M.S.C. 2000: 53C25, 53C55. Key words: Kenmotsu manifold, Killing vector field. §1. Main results Let (M,g) be a Riemannian C ∞ manifold and let ∇ be the covariant differential operator produced by the metric tensor g. We assume that M is oriented. Define Γ(TM )= X M the set of vector fields on M and TM ♭ ⇀ ↽ ♯ T ∗ M be the musical isomor- phisms defined by g, and Ω ♭ : TM → T ∗ M ; the symplectic isomorphism defined by Ω. Following Poor [4] we set A q (M,TM )= HM (∧ q TM,TM ) and notice that ele- ments of A q (M,TM ) are vector valued q-forms. The field of orthonormal frames of an n-dimensional Riemannian manifold is de- noted by O = {e A ; A =1, ..., n} and the associated coframe by O ∗ = {ω A ; A =1, ..., n}. The canonical vector valued 1-form dp of M is called soldering form and is ex- pressed by dp = ω A ⊗ e A . Then E. Cartan’s structure equations in index-full notation are written as ∇e = θ ⊗ e D , Vol.5, No.1, 2003, pp. 23-26. c  Balkan Society of Geometers, Geometry Balkan Press 2003.