41 20 06 v 1 2 7 D ec 1 99 4 On the Scalar Curvature of Complex Surfaces

@inproceedings{Lebrun19954120,
  title={41 20 06 v 1 2 7 D ec 1 99 4 On the Scalar Curvature of Complex Surfaces},
  author={Claude Lebrun},
  year={1995}
}
Let (M, J) be a minimal compact complex surface of Kähler type. It is shown that the smooth 4-manifold M admits a Riemannian metric of positive scalar curvature iff (M,J) admits a Kähler metric of positive scalar curvature. This extends previous results of Witten and Kronheimer. A complex surface is a pair (M,J) consisting of a smooth compact 4-manifold M and a complex structure J on M ; the latter means an almost-complex structure tensor J : TM → TM , J = −1, which is locally isomorphic to the… CONTINUE READING
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