Stability of the Reeb vector field of H-contact manifolds

It is well known that a Hopf vector field on the unit sphere S2n+1 is the Reeb vector field of a natural Sasakian structure on S2n+1. A contact metric manifold whose Reeb vector field. is a harmonic vector field is called an H-contact manifold. Sasakian and K-contact manifolds, generalized (k, mu)-spaces and contact metric three-manifolds with. strongly normal, are H-contact manifolds. In this paper we study, in dimension three, the stability with respect to the energy of the Reeb vector field. for such special classes of H-contact manifolds (and with respect to the volume when. is also minimal) in terms of Webster scalar curvature. Finally, we extend for the Reeb vector field of a compact K-contact (2n+1)-manifold the obtained results for the Hopf vector fields to minimize the energy functional with mean curvature correction.