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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2408.10144 |
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| _version_ | 1866910588944252928 |
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| author | Wang, Ze-Ping Chen, Xue-Yi |
| author_facet | Wang, Ze-Ping Chen, Xue-Yi |
| contents | Inspired by the work of Ou [12,17], we study biharmonic conformal immersions of surfaces into a conformally flat 3-space. We first give a characterization of biharmonic conformal immersions of totally umbilical surfaces into a generic 3-manifold. As an application, we give a method to produce biharmonic conformal immersions into a conformally flat 3-space. We then use the method to obtain a classification of biharmonic maps in a family of conformal immersions and construct many examples of biharmonic conformal immersions from a 2-sphere into a conformal 3-sphere. Our examples include proper biharmonic conformal immersions of a 2-sphere minus a point into a conformal 3-sphere with nonconstant conformal factor and the biharmonic isometric immersion $S^2(\frac{1}{\sqrt{2}})\to S^3$ which was found in [2]. Finally, we study biharmonic conformal immersions of Hopf cylinders of a Riemannian submersion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Biharmonic conformal immersions into a 3-dimensional conformally flat space Wang, Ze-Ping Chen, Xue-Yi Differential Geometry Inspired by the work of Ou [12,17], we study biharmonic conformal immersions of surfaces into a conformally flat 3-space. We first give a characterization of biharmonic conformal immersions of totally umbilical surfaces into a generic 3-manifold. As an application, we give a method to produce biharmonic conformal immersions into a conformally flat 3-space. We then use the method to obtain a classification of biharmonic maps in a family of conformal immersions and construct many examples of biharmonic conformal immersions from a 2-sphere into a conformal 3-sphere. Our examples include proper biharmonic conformal immersions of a 2-sphere minus a point into a conformal 3-sphere with nonconstant conformal factor and the biharmonic isometric immersion $S^2(\frac{1}{\sqrt{2}})\to S^3$ which was found in [2]. Finally, we study biharmonic conformal immersions of Hopf cylinders of a Riemannian submersion. |
| title | Biharmonic conformal immersions into a 3-dimensional conformally flat space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.10144 |