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

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

2010-05-09

arxiv.org/abs/1005.1393v2

Mathematics

Differential Geometry

5 pages

Scientific paper

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 $(k\geq 2)$.

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