A Liouville type theorem for harmonic morphisms

作者：Jung Seoung Dal^*; Liu Huili; Moon Dong Joo

来源：Journal of the Korean Mathematical Society, 2007, 44(4): 941-947.

• harmonic map
• harmonic morphism

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive scalar curvature. Let mu 0 be the least eigenvalue of the Laplacian acting on L-2-functions on M. We show that if Ric(M) >= -mu 0 at all x is an element of M and either Ric(M) >= -mu o at some point chi 0 or Vol(M) is infinite, then every harmonic morphism Phi : M -> N of finite energy is constant.

• 出版日期2007-7
• 单位东北大学