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A fundamental goal of geometry of submanifolds is to find fascinating andsignificant classical examples. In this paper, depending on the theory weestablished in [5], along with the approach we provided for constructingconstant $p$-mean curvature surfaces, we found some interesting examples ofconstant $p$-mean curvature surfaces. In particular, we give a completedescription for rotationally invariant surfaces of constant $p$-mean curvature,including the geometric meaning of the energy $E$ (1.6}.

On invariants of constant $p$-mean curvature surfaces in the Heisenberg group $H_{1}$