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In this paper, we discuss the heat flow of a pseudo-harmonic map from aclosed pseudo-Hermitian manifold to a Riemannian manifold with non-positivesectional curvature, and prove the existence of the pseudo-harmonic map whichis a generalization of Eells-Sampson's existence theorem. We also discuss theuniqueness of the pseudo-harmonic representative of its homotopy class which isa generalization of Hartman theorem, provided that the target manifold hasnegative sectional curvature.

Pseudo-Harmonic Maps From Pseudo-Hermitian Manifolds to Riemannian Manifolds