Local isometric imbedding of a compact Riemann surface with a singular non-CSC extremal Kähler metric into 3-dimension space forms (Q2061542)
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scientific article; zbMATH DE number 7446101
| Language | Label | Description | Also known as |
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| English | Local isometric imbedding of a compact Riemann surface with a singular non-CSC extremal Kähler metric into 3-dimension space forms |
scientific article; zbMATH DE number 7446101 |
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Local isometric imbedding of a compact Riemann surface with a singular non-CSC extremal Kähler metric into 3-dimension space forms (English)
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15 December 2021
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In this article, the authors prove that any singular non-constant scalar curvature extremal Kähler metric, usually called HCMU metric (HCMU means the Hessian of the Curvature of the Metric is Umbilical), can be locally imbedded into a 3-dimensional space form. This result partly answers a question recently raised by \textit{C.-K. Peng} and \textit{Y. Wu} [Result. Math. 75, No. 4, Paper No. 133, 10 p. (2020; Zbl 1447.53014)].
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extremal Kähler metric
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Moving frames
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Hessian of the curvature
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umbilical
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