Critical associated metrics on contact manifolds

David E. Blair
1984 Journal of the Australian Mathematical Society  
Defining a function on the set of all Riemannian metrics associated to a contact form on a compact manifold by taking the integral of the Ricci curvature in the direction of the characteristic vector field, it is shown that on a compact regular contact manifold the only critical points of this function are the metrics for which the characteristic vector field generates a group of isometrics.
doi:10.1017/s1446788700021753 fatcat:7qcqm4deybdgta63fvt5k4nuja