Asian Journal of Mathematics

Volume 17 (2013)

Number 1

On the existence of pseudoharmonic maps from pseudohermitian manifolds into Riemannian manifolds with nonpositive sectional curvature

Pages: 1 – 16



Shu-Cheng Chang (Department of Mathematics, National Taiwan University, Taipei, Taiwan)

Ting-Hui Chang (Institute of Mathematics, Academia Sinica, Taipei, Taiwan)


In this paper, we first derive a CR Bochner identity for the pseudoharmonic map heat flow on pseudohermitian manifolds. Secondly, we are able to prove existence of the global solution for the pseudoharmonic map heat flow from a closed pseudohermitian manifold into a Riemannian manifold with nonpositive sectional curvature. In particular, we prove the existence theorem of pseudoharmonic maps. This is served as the CR analogue of Eells-Sampson’s Theorem for the harmonic map heat flow.


CR Bochner identity, energy density, pseudoharmonic map, pseudoharmonic map heat flow, pseudohermitian manifold, pseudohermitian Ricci tensors, pseudohermitian torsion, sub-Laplacian, Folland-Stein space

2010 Mathematics Subject Classification

Primary 32V05, 32V20. Secondary 53C56.

Published 21 March 2013