# $n$-Harmonicity, Minimality, Conformality and Cohomology

## TL;DR

This paper explores the relationships between cohomology classes, $n$-harmonic morphisms, and $F$-harmonic maps, extending existing theories and providing sharp results on harmonic maps and Riemannian submersions.

## Contribution

It extends previous work on harmonic maps and morphisms by studying cohomology classes related to $n$-harmonic morphisms, introducing new results and revisiting earlier findings.

## Key findings

- Results on $F$-harmonic maps are extended and augmented.
- Theorem 3.2 provides sharp results using the $n$-conservation law.
- Revisits and generalizes previous results on Riemannian submersions and $n$-harmonic morphisms.

## Abstract

By studying cohomology classes that are related with $n$-harmonic morphisms and $F$-harmonic maps, we augment and extend several results on $F$-harmonic maps, harmonic maps in [1, 3, 14], $p$-harmonic morphisms in [17], and also revisit our previous results in [9, 10, 21] on Riemannian submersions and $n$-harmonic morphisms which are submersions. The results, for example Theorem 3.2 obtained by utilizing the $n$-conservation law (2.6), are sharp.