A variational characterization of contact metric structures (Q2673432)

On a manifold with a non-vanishing vector field, the squared \(L^2\)-norm of the integrability tensor of the orthogonal complement of the field is studied as a functional on the space of Riemannian metrics of fixed volume. The first variation of this action is developed for its only critical points. and the second variation of the functional at the critical points is also developed.