Biharmonic and f-biharmonic maps from a 2-sphere

JOURNAL OF GEOMETRY AND PHYSICS

卷:104

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, Dept Math, Commerce, TX 75429 USA

关键词: Biharmonic maps;    f-biharmonic maps;    Conformal change of metrics;    2-sphere;    Riemann sphere;   

DOI  :  10.1016/j.geomphys.2016.02.003

来源: Elsevier

【 摘 要 】

We study biharmonic maps and f-biharmonic maps from the standard sphere (S-2, g(0)), the latter maps are equivalent to biharmonic maps from Riemann spheres (S-2, f(-1)g(0)). We proved that for rotationally symmetric maps between rotationally symmetric spaces, both biharmonicity and f-biharmonicity reduce to a 2nd order linear ordinary differential equation. As applications, we give a method to produce biharmonic maps and f-biharmonic maps from given biharmonic maps and we construct many examples of biharmonic and f-biharmonic maps from the standard sphere S-2 and between two such spheres. Our examples include non-conformal proper biharmonic maps from Riemann spheres (S-2, f(-1)g(0)) -> S-2 and (S-2, f(-1)g(0)) -> S-n, or non-conformal f-biharmonic maps from the standard spheres (S-2, g(0)) -> S-2 and (S-2, g(0)) -> S-n with two singular points. (C) 2016 Elsevier B.V. All rights reserved.

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