Abstract
In this paper, we get a one-parameter family of local isometric immersions from a compact Riemann surface with a singular non-CSC extremal Kähler metric to \({\mathbb {R}}^3\), each of whom is a Weingarten surface. In fact, we can get explicit expressions of the mean curvatures in the family by the Gauss curvature of the metric.
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Acknowledgements
The first author is supported by the National Natural Science Foundation of China (Grant No. 11471299). The second author is supported by the National Natural Science Foundation of China (Grant Nos. 11471308 and 11971450).
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Peng, CK., Wu, Y. A One-Dimensional Singular Non-CSC Extremal Kähler Metric can be Isometrically Imbedded into \({\mathbb {R}}^3\) as a Weingarten Surface. Results Math 75, 133 (2020). https://doi.org/10.1007/s00025-020-01258-5
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DOI: https://doi.org/10.1007/s00025-020-01258-5