  J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed
the first variational formula. When, k=2, it is called biharmonic maps
(2-harmonic maps). There have been extensive studies in the area. In this
paper, We study k-harmonic immersion into a sphere, and get the rerationship
between radious and "k" of k-harmonic. And we also consider k-harmonic
submersion, and genelarize Oniciuc's results. Futhermore we construct non
harmonic k-harmonic by Hopf map.
