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

Details Geometry of k-harmonic maps and the second variational formula of the k-energy Geometry of k-harmonic maps and the second variational formula of the k-energy

2010-03-05

arxiv.org/abs/1003.1258v1

Mathematics

Differential Geometry

20 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 give the second variation formula of k-harmonic maps, and show non-existence theorem of proper k-harmonic maps into a Riemannian manifold of non-positive curvature (k >= 2). We also study k-harmonic maps into the product Riemannian manifold, and describe the ordinary differential equations of 3-harmonic curves and 4-harmonic curves into a sphere, and show their non-trivial solutions.

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