THE LIOUVILLE PROPERTY FOR PSEUDOHARMONIC MAPS WITH FINITE DIRICHLET ENERGY

Abstract

In this paper, we first derive the CR Bochner formula and the CR Kato's inequality for pseudoharmonic maps. Secondly, by applying the CR Bochner formula and the CR Kato's inequality we are able to prove the Liouville property for pseudoharmonic maps with finite Dirichlet energy in a complete $(2n+1)$-pseudohermitian manifold. This is served as CR analogue to the Liouville theorem for harmonic maps in Riemannian Geometry.