We investigate various limits of the twistor spaces associated to the self-dual metrics on nℂℙ2, 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)ℂℙ2, (b) (another) LeBrun metrics on the total space of the line bundle O(-n) over ℂℙ1, (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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics