Contact harmonic maps (Q763056)

The aim of the paper is to continue studies of critical points of the energy functional \(E(\phi)=\frac{1}{2}\int_M Q(\phi) dv\), for \(\phi\in\mathcal{C}^{\infty}(M,N)\), introduced by \textit{R. Petit} in [Ann. Global Anal. Geom. 35, No. 1, 1--37 (2009; Zbl 1175.32018)]. Here \(M\) is a compact strictly pseudoconvex \(CR\) manifold of hypersurface type and \(CR\) dimension \(n\), \(Q(\phi)=\|(d\phi)_{H,H'}\|^2\) and \(dv=\theta\wedge(d\theta)^n\), for a contact form \(\theta\) on \(M\), and both \((M,H)\) and \((N,H')\) are Riemannian contact manifolds; \((d\phi)_{H,H'}\) is the orthogonal projection onto \(H'\) of the restriction to \(H\) of the differential of \(\phi\).