  In this paper, we discuss the heat flow of a pseudo-harmonic map from a
closed pseudo-Hermitian manifold to a Riemannian manifold with non-positive
sectional curvature, and prove the existence of the pseudo-harmonic map which
is a generalization of Eells-Sampson's existence theorem. We also discuss the
uniqueness of the pseudo-harmonic representative of its homotopy class which is
a generalization of Hartman theorem, provided that the target manifold has
negative sectional curvature.
