$n$-Harmonicity, Minimality, Conformality and Cohomology

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.

arXiv comment10 pages, arXiv:2302.14019v[1] 10 pages, arXiv:2302.14019v[1], arXiv:2302.14019v[2], arXiv:2302.14019v[3] 11 pages, to appear in Tamkang Journal of Mathematics