Abstract
In general, we call a one-dimensional singular non-CSC extremal Kähler metric HCMU metric. If an HCMU metric on \(S^2\) just has two singularities, we call this kind of HCMU metrics football. Peng and Wu (Results Math 75:133, 2020) proved that any HCMU metric can be locally isometrically imbedded into \({\mathbb {R}}^3\) as a Weingarten surface. In this paper, we will give a family of local explicit isometric immersions from a football to \({\mathbb {R}}^3\) and prove that there exists a global isometric immersion from a football to \({\mathbb {R}}^3\).
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Acknowledgements
The authors would like to thank Professor Chia-Kuei Peng for his encouragement and helpful discussion.Wu is partially supported by the National Natural Science Foundation of China (Grant No. 11971450) and partially supported by the Project of Stable Support for Youth Team in Basic Research Field, CAS (YSBR-001).
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Wang, K., Wu, Y. Explicit Isometric Immersions from Footballs to \({\mathbb {R}}^3\). Results Math 77, 232 (2022). https://doi.org/10.1007/s00025-022-01760-y
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DOI: https://doi.org/10.1007/s00025-022-01760-y