Communications in Mathematical Physics

, Volume 301, Issue 3, pp 749–770 | Cite as

Degenerations of LeBrun Twistor Spaces

Article

Abstract

We investigate various limits of the twistor spaces associated to the self-dual metrics on \({n \mathbb{CP}^2}\), the connected sum of the complex projective planes, constructed by C. LeBrun. In particular, we explicitly present the following 3 kinds of degenerations whose limits of the corresponding metrics are: (a) LeBrun metrics on \({(n-1) \mathbb{CP}^2}\), (b) (another) LeBrun metrics on the total space of the line bundle \({\fancyscript O(-n)}\) over \({\mathbb{CP}^1}\), (c) the hyper-Kähler metrics on the small resolution of rational double points of type An-1, constructed by G.W. Gibbons and S.W. Hawking.

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Institute of TechnologyMeguro, TokyoJapan
  2. 2.Mathematical Institute, Graduate School of ScienceTohoku UniversitySendaiJapan

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