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Chinese Annals of Mathematics, Series B

, Volume 39, Issue 5, pp 861–878 | Cite as

Biharmonic Maps from Tori into a 2-Sphere

  • Zeping Wang
  • Ye-Lin Ou
  • Hanchun Yang
Article

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 ±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 ±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 

2000 MR Subject Classification

58E20 53C12 

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsYunnan UniversityKunmingChina
  2. 2.Department of MathematicsGuizhou Normal UniversityGuiyangChina
  3. 3.Department of MathematicsTexas A & M University-CommerceCommerceUSA

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