$k$-harmonic maps into a Riemannian manifold with constant sectional curvature
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Abstract:
J. Eells and L. Lemaire introduced $k$-harmonic maps, and Shaobo Wang 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 we show the non-existence theorem of 3-harmonic maps. We also give the definition of $k$-harmonic submanifolds of Euclidean spaces and study $k$-harmonic curves in Euclidean spaces. Furthermore, we give a conjecture for $k$-harmonic submanifolds of Euclidean spaces.References
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Additional Information
- Shun Maeta
- Affiliation: Graduate School of Information Sciences, Tohoku University, Aoba 6-3-09 Aramaki Aoba-ku Sendai-shi Miyagi, 980-8579 Japan
- Address at time of publication: Nakakuki 3-10-9, Oyama-shi, Tochigi, Japan
- MR Author ID: 963097
- Email: shun.maeta@gmail.com
- Received by editor(s): September 19, 2010
- Received by editor(s) in revised form: January 20, 2011, January 27, 2001, and January 29, 2011
- Published electronically: September 26, 2011
- Communicated by: Jianguo Cao
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1835-1847
- MSC (2010): Primary 58E20; Secondary 53C43
- DOI: https://doi.org/10.1090/S0002-9939-2011-11049-9
- MathSciNet review: 2869168