On f-harmonic morphisms between Riemannian manifolds

2011/03/29 by Ou, Ye-Lin
#53C12 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1103.5687

Abstract

f-Harmonic maps were first introduced and studied by Lichnerowicz in \citeLi (see also Section 10.20 in Eells-Lemaire's report \citeEL). In this paper, we study a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions. We prove that a map between Riemannian manifolds is an f-harmonic morphism if and only if it is a horizontally weakly conformal f-harmonic map. This generalizes the well-known Fuglede-Ishihara characterization for harmonic morphisms. Some properties and many examples as well as some non-existence of f-harmonic morphisms are given. We also study the f-harmonicity of conformal immersions.

Related

• Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps
• Pseudo Harmonic Morphisms
• Pseudo-harmonic morphisms with low dimensional fibers
• Harmonic morphisms with one-dimensional fibres on conformally-flat Riemannian manifolds
• Some links between F-harmonicity, submersion and cohomology