Some links between $F$-harmonicity, submersion and cohomology

TL;DR

This paper explores the relationships between $F$-harmonicity, submersions, and cohomology, extending previous results on harmonic maps and morphisms in Riemannian geometry.

Contribution

It introduces new connections between cohomology classes and $F$-harmonic maps, broadening the understanding of harmonic morphisms and submersions.

Findings

Extended results on Riemannian submersions to $F$-harmonic maps

Linked cohomology classes with $p$-harmonic, $F$-harmonic, and $f$-harmonic maps

Generalized previous theorems to broader classes of harmonic maps

Abstract

By studying cohomology classes that are related with $p$-harmonic morphisms, $F$-harmonic maps, and $f$-harmonic maps, we extend several of our previous results on Riemannian submersions and $p$-harmonic morphisms to $F$-harmonic maps, and $f$-harmonic maps which are submersions.