Results in Mathematics

, 74:58 | Cite as

Non-CSC Extremal Kähler Metrics on \({{\varvec{S}}}^2_{\{2,2,2\}}\)

  • Zhiqiang WeiEmail author
  • Yingyi Wu


We often call an extremal Kähler metric with finite singularities on a compact Riemann surface an HCMU (the Curvature of the Metric is Umbilical) metric. In this paper, we construct all of the normalized non-CSC HCMU metrics on \(S^2_{\{2,2,2\}}\) by proving the existence of some kind of meromorphic 1-forms on the Riemann sphere \(S^{2}\).


Extremal Kähler metric conical singularities constant curvature 

Mathematics Subject Classification

53C56 53C21 



The authors would like to express their deep gratitude to the referees for their very valuable comments on improving the whole paper. Wei thanks Professors C. K. Peng and X. X. Jiao for their warm encouragements for during the past 5 years. This work is also supported by the National Natural Science Foundation of China (Grant No. 11871450).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHenan UniversityKaifengPeople’s Republic of China
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China

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