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Communications in Mathematical Physics

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

Degenerations of LeBrun Twistor Spaces

  • Nobuhiro HondaEmail author
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 A n-1, constructed by G.W. Gibbons and S.W. Hawking.

Keywords

Line Bundle Irreducible Component Real Structure Projective Model Normal Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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