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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Non-existence of quadratic harmonic maps of $ S^{4}$ into $ S^{5}$ or $ S^{6}$


Authors: Faen Wu and Xinnuan Zhao
Journal: Proc. Amer. Math. Soc. 141 (2013), 1083-1091
MSC (2010): Primary 58E20; Secondary 53C43
Published electronically: July 16, 2012
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Abstract: In this paper, we settle the last two open cases of non-existence of full quadratic harmonic maps from $ S^{4}$ to $ S^{5}$ or $ S^{6}$. Assume that there exist full quadratic harmonic maps from $ S^{4}$ to $ S^{n}$ for some integer $ n$. As a consequence of our theorem we obtain that the sufficient and necessary condition of the existence of such maps is that $ n$ satisfy $ 4\leq n\leq 13$ and $ n\neq 5,6$.


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Additional Information

Faen Wu
Affiliation: Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, People’s Republic of China, 100044
Email: fewu@bjtu.edu.cn

Xinnuan Zhao
Affiliation: Guangxi University of Technology, Lushan College, Liuzhou, People’s Republic of China, 545616
Email: 06121962@bjtu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11460-1
PII: S 0002-9939(2012)11460-1
Keywords: Quadratic harmonic map, $n$-dimensional sphere, Euclidean space
Received by editor(s): July 19, 2011
Published electronically: July 16, 2012
Additional Notes: The first author is supported by NSFC No. 11171016
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.