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| Biharmonic Maps from Tori into a 2-Sphere |
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Citation： |
Zeping WANG,Ye-Lin OU,Hanchun YANG.Biharmonic Maps from Tori into a 2-Sphere[J].Chinese Annals of Mathematics B,2018,39(5):861~878 |
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Net amount： 1029 |
Authors： |
Zeping WANG; Ye-Lin OU;Hanchun YANG |
Foundation： |
The third author was supported by the Natural Science
Foundation of China (No.11361073) and the second author was
supported by the Natural Science Foundation of Guangxi Province of
China (No.2011GXNSFA018127). |
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| Abstract： |
Biharmonic maps are generalizations of harmonic maps. A well-known
result 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. The authors 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. The results in this
paper show that there exists no proper biharmonic maps of degree
$\pm 1$ in a large family of maps from a torus into a sphere. |
Keywords： |
Biharmonic maps, Biharmonic tori, Harmonic maps, Gauss maps, Maps into a sphere |
Classification： |
58E20, 53C12 |
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