Science China Mathematics

, Volume 62, Issue 11, pp 2195–2210 | Cite as

A note on the collapsing geometry of hyperkähler four manifolds

  • Shouhei Honda
  • Song SunEmail author
  • Ruobing Zhang


We make some observations concerning the one-dimensional collapsing geometry of four-dimensional hyperkähler metrics.


hyperkähler metrics collapsing K3 manifold 


53C25 51P05 



The first author was supported by the Grantin-Aid for Young Scientists (B) (Grant No. 16K17585) and Grant-in-Aid for Scientific Research (B) (Grant No. 18H01118). The second author was supported by National Science Foundation of USA (Grant No. DMS-1916520) and the Simons Collaboration Grant on Special Holonomy in Geometry, Analysis and Physics (Grant No. 488633, S.S.). The third author was supported by National Science Foundation of USA (Grant No. DMS-1906265).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  3. 3.Department of MathematicsStony Brook UniversityStony BrookUSA

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