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

TL;DR

This paper studies the heat flow of pseudo-harmonic maps from pseudo-Hermitian manifolds to Riemannian manifolds, establishing existence and uniqueness results that generalize classical theorems in harmonic map theory.

Contribution

It extends Eells-Sampson's and Hartman's theorems to the setting of pseudo-harmonic maps between pseudo-Hermitian and Riemannian manifolds.

Findings

Proves existence of pseudo-harmonic maps under non-positive curvature conditions.

Establishes uniqueness of pseudo-harmonic representatives in homotopy classes with negative curvature.

Generalizes classical harmonic map theorems to pseudo-Hermitian contexts.

Abstract

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.