Duke Mathematical Journal

Explicit construction of self-dual 4-manifolds

Dominic D. Joyce

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 77, Number 3 (1995), 519-552.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077286532

Digital Object Identifier
doi:10.1215/S0012-7094-95-07716-3

Mathematical Reviews number (MathSciNet)
MR1324633

Zentralblatt MATH identifier
0855.57028

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 32L25: Twistor theory, double fibrations [See also 53C28] 53A30: Conformal differential geometry 53C05: Connections, general theory

Citation

Joyce, Dominic D. Explicit construction of self-dual $4$ -manifolds. Duke Math. J. 77 (1995), no. 3, 519--552. doi:10.1215/S0012-7094-95-07716-3. https://projecteuclid.org/euclid.dmj/1077286532


Export citation

References

  • [1] A. Ashtekar, T. Jacobson, and L. Smolin, A new characterization of half-flat solutions to Einstein's equation, Comm. Math. Phys. 115 (1988), no. 4, 631–648.
  • [2] M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978), no. 1711, 425–461.
  • [3] W. G. Brown, Historical note on a recurrent combinatorial problem, Amer. Math. Monthly 72 (1965), 973–977.
  • [4] J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded. I, J. Differential Geom. 23 (1986), no. 3, 309–346.
  • [5] G. W. Gibbons and S. W. Hawking, Gravitational multi-instantons, Phys. Lett. B 78 (1978), 430–432.
  • [6] P. E. Jones and K. P. Tod, Minitwistor spaces and Einstein-Weyl spaces, Classical Quantum Gravity 2 (1985), no. 4, 565–577.
  • [7] D. D. Joyce, The hypercomplex quotient and the quaternionic quotient, Math. Ann. 290 (1991), no. 2, 323–340.
  • [8] D. Joyce, Hypercomplex and quaternionic manifolds, part I, Ph.D. thesis, Oxford, 1992.
  • [9] C. LeBrun, Explicit self-dual metrics on $\bf C\rm P\sb 2\#\cdots\#\bf C\rm P\sb 2$, J. Differential Geom. 34 (1991), no. 1, 223–253.
  • [10] L. J. Mason and E. T. Newman, A connection between the Einstein and Yang-Mills equations, Comm. Math. Phys. 121 (1989), no. 4, 659–668.
  • [11] P. Orlik and F. Raymond, Actions of the torus on $4$-manifolds. I, Trans. Amer. Math. Soc. 152 (1970), 531–559.
  • [12] P. Orlik and F. Raymond, Actions of the torus on $4$-manifolds. II, Topology 13 (1974), 89–112.
  • [13] Y. Sun Poon, Compact self-dual manifolds with positive scalar curvature, J. Differential Geom. 24 (1986), no. 1, 97–132.
  • [14] Y. Sun Poon, Algebraic dimension of twistor spaces, Math. Ann. 282 (1988), no. 4, 621–627.
  • [15] S. M. Salamon, Differential geometry of quaternionic manifolds, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 1, 31–55.
  • [16] C. H. Taubes, The existence of anti-self-dual conformal structures, J. Differential Geom. 36 (1992), no. 1, 163–253.