TY - JOUR

T1 - Degenerations of LeBrun Twistor Spaces

AU - Honda, Nobuhiro

N1 - Funding Information:
The author has been partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.

PY - 2011/2

Y1 - 2011/2

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-010-1165-x

DO - 10.1007/s00220-010-1165-x

M3 - Article

AN - SCOPUS:79951515756

VL - 301

SP - 749

EP - 770

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -