Contact harmonic maps

We study contact harmonic maps, i.e. smooth maps ϕ:M→N from a strictly pseudoconvex CR manifold M into a contact Riemannian manifold N which are critical points of the functional E(ϕ)=12∫M‖(dϕ)H,H′‖2θ∧(dθ)n and their generalizations. We derive the first and second variation formulae for E and study stability of contact harmonic maps. Contact harmonic maps are shown to arise as boundary values of critical points ϕ∈C∞(Ω¯,N) of the functional ∫Ω‖ΠH′ϕ∘ϕ⁎‖2dvol(gB) where Ω⊂Cn+1 is a smoothly bounded strictly pseudoconvex domain endowed with the Bergman metric gB.