On the Scalar Curvature of Complex Surfaces

Claude LeBrun

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arXiv · dg-ga/9412006

On the Scalar Curvature of Complex Surfaces

Claude LeBrun

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Abstract

Let (M,J) be a minimal compact complex surface of Kaehler type. It is shown that the smooth 4-manifold M admits a Riemannian metric of positive scalar curvature iff (M,J) admits a KAEHLER metric of positive scalar curvature. This extends previous results of Witten and Kronheimer.

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Claude LeBrun. 1994-12-27. On the Scalar Curvature of Complex Surfaces. https://arxiv.org/abs/dg-ga/9412006

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