$n$-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 obtaine by utilizing the n-conservation law (2.6), are sharp.