Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory

Claude LeBrun

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arXiv · math/9803093

Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory

Claude LeBrun

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Abstract

We show that solutions of the Seiberg-Witten equations lead to non-trivial lower bounds for the L2-norm of the Weyl curvature of a compact Riemannian 4-manifold. These estimates are then used to derive new obstructions to the existence of Einstein metrics. These results considerably refine those previously obtained using scalar-curvature estimates alone.

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BibTeX RIS

Claude LeBrun. 1998-04-15. Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory. https://arxiv.org/abs/math/9803093

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