A Theorem of Liouville Type for p-Harmonic Morphisms

摘要

In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if φ: M → N is a p-harmonic morphism (p ≥ 2) from a complete noncompact Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of nonpositive scalar curvature such that the p-energy E_p(φ), or (2p-2)-energy E_(2p-2)(φ) is finite, then φ is constant.