TY - JOUR
T1 - Degenerations of LeBrun Twistor Spaces
AU - Honda, Nobuhiro
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
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 -