In this paper, we investigate a class of metrics induced by F-natural metrics on the indicatrix bundle of a Finsler manifold. This class constitutes a four-parameter family that generalizes the well-known g-natural metrics on the unit tangent bundle of a Riemannian manifold. Within this framework, we construct a three-parameter family of contact metric structures whose associated metrics are F-natural, and we establish that, in contrast to the Riemannian case —where all such K-contact metrics on unit tangent bundles are necessarily Sasakian— the corresponding structures in the Finslerian setting can be K-contact without being Sasakian. Furthermore, we provide a characterization of Finsler manifolds with positive constant flag curvature via the existence of K-contact structures on their indicatrix bundles.
Abbassi et al. (Mon,) studied this question.