Abstract
A non-CSC extremal Kähler metric with finite singularities on a compact Riemann surface is often called HCMU metric. In Peng and Wu (Results Math 75:133, 2020) the authors proved that an HCMU metric can be locally isometrically imbedded into \(\mathbb {R}^3\) as a Weingarten surface. In this paper, we will give a classification of local isometric immersions into \(\mathbb {R}^3\) as Weingarten surfaces of an HCMU metric.
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Acknowledgements
The authors would like to thank Professor C.K. Peng for his encouragement and helpful discussion. The first author is supported by Natural Science Foundation of Henan (No.202300410067). The second author is supported by National Natural Science Foundation of China (No.11971450) and by National Key Research and Development Program of China (No.2020YFA0713703).
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Wei, Z., Wu, Y. HCMU Surfaces and Weingarten Surfaces. J Geom Anal 32, 199 (2022). https://doi.org/10.1007/s12220-022-00933-z
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DOI: https://doi.org/10.1007/s12220-022-00933-z