Asian Journal of Mathematics
Volume 17 (2013)
On the existence of pseudoharmonic maps from pseudohermitian manifolds into Riemannian manifolds with nonpositive sectional curvature
Pages: 1 – 16
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.