Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 52, Number 1 (2000), 139-160.
A Kummer type construction of self-dual metrics on the connected sum of four complex projective planes
We show that there exist on , the connected sum of four complex projective planes, self-dual metrics with the following properties: (i) the sign of the scalar curvature is positive, (ii) the identity component of the isometry group is the metrics are not conformally isometric to the self-dual metrics constructed by LeBrun [LB1]. These are the first examples of self-dual metrics with non semi-free isometries on simply connected manifolds. Our proof is based on the twistor theory: we use an equivariant orbifold version of the construction of Donaldson and Friedman [DF]. We also give a rough description of the structure of the algebraic reduction of the corresponding twistor spaces.
J. Math. Soc. Japan Volume 52, Number 1 (2000), 139-160.
First available in Project Euclid: 10 June 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32L25: Twistor theory, double fibrations [See also 53C28]
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
HONDA, Nobuhiro; ITOH, Mitsuhiro. A Kummer type construction of self-dual metrics on the connected sum of four complex projective planes. J. Math. Soc. Japan 52 (2000), no. 1, 139--160. doi:10.2969/jmsj/05210139. https://projecteuclid.org/euclid.jmsj/1213107660