Exponentially harmonic maps, Morse index and Liouville type theorems (Q2663788)

The author obtains a result on the Morse index of an exponentially harmonic map from a Riemannian manifold into the unit \(n\)-sphere, and further derives a Liouville type 1 theorem for exponentially harmonic maps between two Riemannian manifolds. Finally, under certain conditions, for a complete Riemannian manifold \((M,g_0)\) with a pole \(x_0\) and a Riemannian manifold \((N,h)\), a Liouville type 2 theorem for exponentially harmonic maps \(f:(M,\rho^2 g_0)\to N\), \(0<ρ\in C^{\infty}(M)\), is proved.