Biharmonic and -biharmonic maps from a 2-sphere

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• 作者：Ze-Ping Wang^a ; ^{zpwzpw2012@126.com" class="auth_mail" title="E-mail the corresponding author} ; Ye-Lin Ou^b ; ^{yelin.ou@tamuc.edu" class="auth_mail" title="E-mail the corresponding author} ; Han-Chun Yang^a ; ^{hyang@ynu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：58E20 ; 53C43
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：104
• 期：Complete
• 页码：137-147
• 全文大小：441 K

文摘

We study biharmonic maps and f$f$-biharmonic maps from the standard sphere (S²,g₀)$(S^2,g_0)$, the latter maps are equivalent to biharmonic maps from Riemann spheres (S²,f⁻¹g₀)$(S^2,f^{-1}{g}_0)$. We proved that for rotationally symmetric maps between rotationally symmetric spaces, both biharmonicity and f$f$-biharmonicity reduce to a 2nd order linear ordinary differential equation. As applications, we give a method to produce biharmonic maps and f$f$-biharmonic maps from given biharmonic maps and we construct many examples of biharmonic and f$f$-biharmonic maps from the standard sphere S²$S^2$ and between two such spheres. Our examples include non-conformal proper biharmonic maps from Riemann spheres 30e9bd0a7fe82a" title="Click to view the MathML source">(S²,f⁻¹g₀)⟶S²$(S^2,f^{-1}{g}_0)⟶S^2$ and (S²,f⁻¹g₀)⟶Sⁿ$(S^2,f^{-1}{g}_0)⟶S^n$, or non-conformal f$f$-biharmonic maps from the standard spheres (S²,g₀)⟶S²$(S^2,g_0)⟶S^2$ and (S²,g₀)⟶Sⁿ$(S^2,g_0)⟶S^n$ with two singular points.