HCMU Surfaces and Weingarten Surfaces

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 R 3 as a Weingarten surface. In this paper, we will give a...

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Veröffentlicht in:	The Journal of Geometric Analysis 2022-07, Vol.32 (7), Article 199
Hauptverfasser:	Wei, Zhiqiang, Wu, Yingyi
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Riemann surfaces
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Zusammenfassung:	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 R 3 as a Weingarten surface. In this paper, we will give a classification of local isometric immersions into R 3 as Weingarten surfaces of an HCMU metric.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-022-00933-z