k-harmonic maps into a Riemannian manifold with constant sectional curvature

Abstract

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 consider the relationship between biharmonic maps and k-harmonic maps, and show non-existence theorem of 3-harmonic maps. We also give the definition of k-harmonic submanifolds of Euclidean spaces, and study k-harmonic curve in Euclidean spaces. Futhermore, we give a conjecture for k-harmonic submanifolds of Euclidean spaces.

8 pages

References in corpus (2)

• The second variational formula of the k-energy and k-harmonic curves
• Geometry of k-harmonic maps and the second variational formula of the k-energy

Cited by in corpus (1)

• k-Harmonic immersion and submersion into a sphere