Non-existence of quadratic harmonic maps of into or

Authors:
Faen Wu and Xinnuan Zhao

Journal:
Proc. Amer. Math. Soc. **141** (2013), 1083-1091

MSC (2010):
Primary 58E20; Secondary 53C43

DOI:
https://doi.org/10.1090/S0002-9939-2012-11460-1

Published electronically:
July 16, 2012

MathSciNet review:
3003698

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we settle the last two open cases of non-existence of full quadratic harmonic maps from to or . Assume that there exist full quadratic harmonic maps from to for some integer . As a consequence of our theorem we obtain that the sufficient and necessary condition of the existence of such maps is that satisfy and .

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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:
https://doi.org/10.1090/S0002-9939-2012-11460-1

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.