@MISC{Fu_theclassification, author = {Ji-xiang Fu}, title = {The Classification of Harmonic Morphisms to Euclidean Space}, year = {} }

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Abstract

Introduction Harmonic morphism is a smooth map between Riemannian manifolds which pulls back germs of harmonic functions to germs of harmonic functions. It may be charactrized as harmonic maps which are horizontally weakly conformal [5,9]. One task of studying harmonic morphism is constructing concrete examples; Another one is classication of all harmonic morphisms between all special manifolds (in particularly, between connected open set of space forms), see for example [6] and [10]. In particularly, we have Theorem 1.1. [10] Let : R m ! N n (n 3) be a harmonic morphism with totally geodesic bers. Then N = R n and is an orthogonal projection P : R m ! R n , followed by a homothety. Theorem 1.2. [6]