  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.

Differential Geometry