Summary: If \(dp\) denotes the soldering form of a differentiable \(C^\infty\) manifold (i.e. the canonical vector valued 1-form) and \(\nabla\) the covariant differential operators, then a TF may be defined as \[ \nabla{\mathcal T}=sdp+\omega{\mathcal T},\quad s\in \Lambda^0M \] where \(\omega\in\Lambda^1M\) is the associated Pfaffian with \(\mathcal T\). It is shown that if the a vector field \(W= \omega^\sharp\) of a torse forming vector field (TF) is a skew symmetric Killing vector field, then the TF is an exterior concurrent vector field. Further the existence of an horizontal TF on a Kenmotsu manifold (\(\omega K\)-manifold) \(M (\varphi, \Omega, \eta,\xi,g)\) [\textit{I. Mihai, R. Rosca} and \textit{L. Verstraelen}, Some aspects of the differential geometry of vector fields, Kath. Univ. Leuven, Kath. Univ. Brussels, Padge 2 (1996; Zbl 0960.53019)] is proved by considering a closed differential system. If \({\mathcal T}_1\) and \({\mathcal T}_2\) are two such TF having both the same structure 1-form \(\eta\) as associated Pfaffian, it is proved that \(M\) is foliated by surfaces tangent to \({\mathcal T}_1\) and \({\mathcal T}_2\). Other properties of torse forming vector fields are also discussed.