A theorem of Liouville type for \(p\)-harmonic morphisms (Q1419405)

This paper generalizes a remark on harmonic morphisms proved by the same authors [Geom. Dedicata 84, 179--182 (2001; Zbl 0980.58010)] to the case of \(p\)-harmonic morphisms, \(p\geq2\). It is proved that any \(p\)-harmonic morphism from a complete noncompact Riemannian manifold of nonnegative Ricci curvature to a Riemannian manifold of nonpositive scalar curvature has to be constant if it has finite \(p\)-energy or finite \((2p-2)\)-energy. The proof uses the Bochner technique.