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

Shun Maeta

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

Differential Geometry 2010-06-09 v2

Authors: Shun Maeta

Abstract

J.Eells and L. Lemaire introduced k-harmonic maps, and T. Ichiyama, J. Inoguchi and H.Urakawa showed the first variation formula. In this paper, we describe the ordinary differential equations of $3$ -harmonic curves into a Riemannian manifold with constant sectional curvature, and show biharmonic curve is k-harmonic curve $(k\geq 2)$ .

Keywords

k-harmonic map biharmonic curve Riemannian manifold constant sectional curvature ordinary differential equation

Cite

@article{arxiv.1005.1393,
  title  = {k-harmonic curves into a Riemannian manifold with constant sectional curvature},
  author = {Shun Maeta},
  journal= {arXiv preprint arXiv:1005.1393},
  year   = {2010}
}

Comments

5 pages

Related papers

View all related →