Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory

Details Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory

1998-03-20

arxiv.org/abs/math/9803093v2

Mathematics

Differential Geometry

17 pages. LaTeX2e. Revised version improves estimates, simplifies proofs, and gives cleaner applications

Scientific paper

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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