By means of multi-Hamiltonians, it can be proved that a conformal and extended harmonic map between connected Riemannian manifolds is homothetic. Also, it is proved that a conformal and extended harmonic map of a connected, compact Riemannian manifold without boundary to a connected Riemannian manifold is harmonic under a certain condition, by making use of the divergences of stress-energy tensors.

Lagrange equations, Hamiltonians, extended harmonic map.