Scalar curvature and connected sums of self-dual 4-manifolds

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Kalafat M.

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, vol.13, no.4, pp.883-898, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.4171/jems/269
  • Journal Name: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.883-898
  • Middle East Technical University Affiliated: No

Abstract

Under a reasonable vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-manifolds is again self-dual. Here we prove that the same result can be extended to the positive scalar curvature case. This is an analogue of the classical theorem of Gromov-Lawson and Schoen-Yau in the self-dual category. The proof is based on twistor theory.