https://hal-uphf.archives-ouvertes.fr/hal-03149449Ghandour, ElsaElsaGhandourLMCPA - Laboratoire des Matériaux Céramiques et Procédés Associés - EA 2443 - UVHC - Université de Valenciennes et du Hainaut-Cambrésis - INSA Hauts-De-France - INSA Institut National des Sciences Appliquées Hauts-de-FranceOu, Ye-LinYe-LinOuGeneralized harmonic morphisms and horizontally weakly conformal biharmonic mapsHAL CCSD2018Generalized harmonic morphismsHarmonic morphismsBiharmonic mapsBiharmonic morphismsHorizontally weakly conformal maps[SPI] Engineering Sciences [physics][MATH] Mathematics [math]Cagniard, Julie2021-02-23 09:31:292022-01-21 03:26:382021-02-23 09:31:29enJournal articles10.1016/j.jmaa.2018.04.0441Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several areas in mathematics (see the book [2] by Baird and Wood for details). In this paper, we study generalized harmonic morphisms which are defined to be maps between Riemannian manifolds that pull back harmonic functions to biharmonic functions. We obtain some characterizations of generalized harmonic morphisms into a Euclidean space and give two methods of constructions that can be used to produce many examples of generalized harmonic morphisms which are not harmonic morphisms. We also give a complete classification of generalized harmonic morphisms among the projections of a warped product space, which provides infinitely many examples of proper biharmonic Riemannian submersions and conformal submersions from a warped product manifold.