Shun Maeta
Published 2010-05-09, updated 2010-06-08Version 2
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 $(k\geq 2)$.
Hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$ with constant sectional curvature
Differential geometry of curves and manifolds with constant sectional curvature
The vectorial Ribaucour transformation for submanifolds of constant sectional curvature
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