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A Theorem of Liouville Type for Harmonic Morphisms
Geometriae Dedicata, 2001Let \(M\) be a complete noncompact Riemannian manifold with nonnegative Ricci curvature and \(N\) be a Riemannian manifold with nonpositive scalar curvature. Then every harmonic morphism \(M\to N\) of finite energy is constant. This theorem is related to the classical result of \textit{R. Schoen} and \textit{S.-T. Yau} [Comment. Math. Helv. 51, 333-341
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