Descrip.

RESUMEN In the case of real functions of several variables harmonicity of the function implies harmonicity of the components and therefore the property extends to the differential as a function between the corresponding tangent bundles. This problem can be open to arbitrary Riemannian or ( pseudo-Remannian) manifolds (M,g) and (N,h) considering on its tangent bundles T M and T N the corresponding complete lift metrics G^c and H^c respectively. We obtain that the harmonicity of the maps F: (M,g) --------> (N,g) is equivalent to the df : (TM G^c) ----->(T N H^c). This rsult gives examples of harmonic maps between pseudo-Remannian manifolds.