Subelliptic Biharmonic Maps

We study subelliptic biharmonic maps, i.e., smooth maps ϕ: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 ϕ:M→N is a subelliptic biharmonic map if and only if its vertical lift ϕ∘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).