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

By S. Maeta. 2010

54 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7590050259ac705fb8edc6998da889d57080708e

How researchers see this paper

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In Applied Mathematics

1. Marian Ioan Munteanu
2. Bang‐Yen Chen
3. Ion Mihai
4. Bayram Sahin
5. I. Hasegawa
6. Siraj Uddin

In Astronomy and Astrophysics

1. Bang‐Yen Chen
2. Marian Ioan Munteanu
3. Bayram Sahin

In Geometry and Topology

1. Marian Ioan Munteanu
2. Bang‐Yen Chen
3. Ion Mihai
4. I. Hasegawa

Citations in the corpus

• Biharmonic ideal hypersurfaces in Euclidean spaces (2013, background): “Maeta [25] found some relations between k-harmonic and harmonic maps of Riemannian manifolds into non-flat real space forms.”