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arXiv · 1310.0562

Biharmonic maps from a 2-sphere

Ze-Ping Wang·Ye-Lin Ou·Han-Chun Yang
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Abstract

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 $S^2\longrightarrow (N^n, h)$ be a weakly conformal immersion.

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Ze-Ping Wang, Ye-Lin Ou, Han-Chun Yang. 2013-10-02. Biharmonic maps from a 2-sphere. https://doi.org/10.1016/j.geomphys.2013.12.005

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