Abstract: In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR) Yamabe problem, Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg group $\mathbb H^n$ by using the computer in [5]. They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae. With the help of dimension conservation and invariant tensors, we can answer the above question.

Key words: Cauchy-Riemann Yamabe problem, subelliptic equations, Jerison-Lee identities