Abstract
Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive scalar curvature. Let μ0 be the least eigenvalue of the Laplacian acting on L2-functions on M . We show that if RicM ≥ −μ0 at all x ∈ M and either RicM > −μ0 at some point x0 or Vol(M) is infinite, then every harmonic morphism φ : M → N of finite energy is constant.
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