It is known since the work of Chern and Hamilton that every contact 1-form defined on a 3-manifold admits an adapted Riemannian metric. A natural problem which arises is whether we can characterize properties of metrics adapted to tight or overtwisted contact structures. In this talk I will present a theorem which provides such a characterization for tight contact forms admitting a regular Killing contact vector field. As a consequence of this result one may construct new examples of energy minimizing steady Euler fluid flows on principal S^1 -bundles. This methodology also gives progress towards the conjecture that contact structures on Seifert fibered manifolds, which are transverse to the fibres, always define tight energy minimizers. During the talk I will provide the necessary background material.