Biharmonic maps from a 2-sphere

JOURNAL OF GEOMETRY AND PHYSICS

卷:77

Article

Wang, Ze-Ping¹  Ou, Ye-Lin²  Yang, Han-Chun¹ 

[1] Yunnan Univ, Dept Math, Kunming 650091, Peoples R China

[2] Texas A&M Univ Commerce, Dept Math, Commerce, TX 75429 USA

关键词: Biharmonic maps;    Warped product metrics;    2-spheres;    Rotationally symmetric map;    Rotationally symmetric manifolds;   

DOI  :  10.1016/j.geomphys.2013.12.005

来源: Elsevier

【 摘 要 】

Motivated by the rich theory of harmonic maps from a 2-sphere, we study biharmonic maps from a 2-sphere in this paper. We first derive biharmonic equation for rotationally symmetric maps between rotationally symmetric 2-manifolds. We then apply the equation to obtain a classification of biharmonic maps in a family of rotationally symmetric maps between 2-spheres. We also find many examples of proper biharmonic maps defined locally on a 2-sphere. Our results seem to suggest that any biharmonic map S-2 -> (N-n, h) is a weakly conformal immersion. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free