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arXiv · 1406.4910

Biharmonic maps from tori into a 2-sphere

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

Biharmonic maps are generalizations of harmonic maps. A well-known result of Eells and Wood on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere (whatever the metrics chosen) in the homotopy class of maps of Brower degree $\pm 1$. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. In this paper, we obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. Our results show that there exists no proper biharmonic maps of degree $\pm 1$ in a large family of maps from a torus into a sphere.

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Ze-Ping Wang, Ye-Lin Ou, Han-Chun Yang. 2014-06-18. Biharmonic maps from tori into a 2-sphere. https://arxiv.org/abs/1406.4910

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