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On the topology of self-dual $ 4$-manifolds

Author: Claude LeBrun
Journal: Proc. Amer. Math. Soc. 98 (1986), 637-640
MSC: Primary 53C25; Secondary 32J99, 57R15
MathSciNet review: 861766
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Abstract: Obstructions are obtained for the problem of finding a Riemannian metric with self-dual conformal curvature and nonnegative scalar curvature on a given smooth compact $ 4$-manifold. A list is given of those simply connected manifolds conceivably admitting such metrics.

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  • [1] N. Hitchin, private communication; Y. S. Poon, D. Phil. Thesis, Oxford, 1985.
  • [2] R. Schoen, Conformal deformation of metrics to constant scalar curvature, J. Differential Geom. 20 (1984), 479-495. MR 788292 (86i:58137)
  • [3] N. Hitchin, Harmonic spinors, Adv. Math. 14 (1974), 1-55. MR 0358873 (50:11332)
  • [4] M. Atiyah, N. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London. Ser. A 362 (1978), 425-461. MR 506229 (80d:53023)
  • [5] S. T. Yau, On the Ricci curvature of a compact Kähler manifold, Comm. Pure. Appl. Math. 31 (1978), 339-411. MR 480350 (81d:53045)
  • [6] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, 1978. MR 507725 (80b:14001)
  • [7] S. T. Yau, On the curvture of compact Hermitian manifolds, Invent. Math. 25 (1974), 213-239. MR 0382706 (52:3588)
  • [8] D. Freed and K. Uhlenbeck, Instantons and four-manifolds, Springer-Verlag, 1985. MR 1081321 (91i:57019)

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Article copyright: © Copyright 1986 American Mathematical Society

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