On stability of exponentially subelliptic harmonic maps

In this paper, we study the stability problem of exponentially subelliptic harmonic maps from sub-Riemannian manifolds to Riemannian manifolds. We derive the rst and second variation formulas for exponentially subelliptic harmonic maps, and apply these formulas to prove that if the target manifold has nonpositive curvature, the exponentially subelliptic harmonic map is stable. Further, we obtain the instability of exponentially subelliptic harmonic maps when the target manifold is a sphere.