Q-curvature operators on differential forms in CR geometry


    Jeffrey Case
    Pennsylvania State University


We introduce Q-curvature operators on closed and CR-closed differential forms on CR manifolds. Among the properties of these operators are that they satisfy a linear conformal transformation formula and that they give rise to CR invariant “Hodge theorems”. We describe these properties and apply them to partially solve the problem of finding contact forms with critical Q-curvature equal to zero.