Subelliptic Biharmonic Maps

We study subelliptic biharmonic maps, i.e., smooth maps ?:M→N from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of the energy functional $E_{2,b} (phi ) = frac{1}{2} int_{M} | tau_{b} (phi ) |^{2} theta wedge (d theta)^{n}$ . We show that ?:M→N is a subelliptic biharmonic map if and only if its vertical lift ?°π:C(M)→N to the (total space of the) canonical circle bundle $S^{1} to C(M) stackrel{pi}{longrightarrow} M$ is a biharmonic map with respect to the Fefferman metric F _θ on C(M).