Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Self-duality and differentiable structures on the connected sum of complex projective planes

Authors: Henrik Pedersen and Yat Sun Poon
Journal: Proc. Amer. Math. Soc. 121 (1994), 859-864
MSC: Primary 32L25; Secondary 32J17, 53C56, 57R55
MathSciNet review: 1195729
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that if the twistor space of a self-dual four-manifold of positive scalar curvature contains a real effective divisor of degree two, then the four-manifold is diffeomorphic to the connected sum $ n\mathbb{C}{P^2}$ of n complex projective planes for some n. It follows that if the four-manifold is known to be homeomorphic to $ 4\mathbb{C}{P^2}$, then it is also diffeomorphic to $ 4\mathbb{C}{P^2}$.

References [Enhancements On Off] (What's this?)

  • [1] F. Campana, On twistor spaces of the class $ \mathcal{C}$, J. Differential Geom. 33 (1991), 541-549. MR 1094468 (92g:32059)
  • [2] S. K. Donaldson and R. Friedman, Connected sums of self-dual manifolds and deformations of singular spaces, Nonlinearity 2 (1989), 197-239. MR 994091 (90e:32027)
  • [3] A. Floer, Self-dual conformal structure on $ \ell C{P^2}$, J. Differential Geom. 33 (1991), 551-574. MR 1094469 (92e:53049)
  • [4] N. J. Hitchin, Linear field equations on self-dual spaces, Proc. London Math. Soc. (3) A370 (1980), 173-191. MR 563832 (81i:81057)
  • [5] -, Kählerian twistor spaces, Proc. London Math. Soc. (3) 3 (1981), 133-150. MR 623721 (84b:32014)
  • [6] C. LeBrun, Explicit self-dual metrics on $ C{P_2}\char93 \cdots \char93 C{P_2}$, J. Differential Geom. 34 (1991), 223-254. MR 1114461 (92g:53040)
  • [7] C. LeBrun and Y. S. Poon, Twistors, Kähler manifolds and bimeromorphic geometry. II, J. Amer. Math. Soc. 5 (1992), 317-325. MR 1137099 (92m:32053)
  • [8] Y. S. Poon, Compact self-dual manifolds with positive scaler curvature, J. Differential Geom. 24 (1986), 97-132. MR 857378 (88b:32022)
  • [9] -, On the algebraic dimension of twistor spaces, Math. Ann. 282 (1988), 621-627. MR 970223 (90f:32029)
  • [10] -, On the algebraic structure of twistor spaces, J. Differential Geom. 36 (1992), 451-491. MR 1180390 (94a:32045)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32L25, 32J17, 53C56, 57R55

Retrieve articles in all journals with MSC: 32L25, 32J17, 53C56, 57R55

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society