Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory
نویسنده
چکیده
We show that solutions of the Seiberg-Witten equations lead to nontrivial estimates for the L-norm of the Weyl curvature of a smooth compact 4-manifold. These estimates are then used to derive new obstructions to the existence of Einstein metrics on smooth compact 4-manifolds with a non-zero Seiberg-Witten invariant. These results considerably refine those previously obtained [21] by using scalar-curvature estimates alone.
منابع مشابه
WEYL CURVATURE , EINSTEIN METRICS , AND SEIBERG - WITTEN THEORY Claude LeBrun
We show that solutions of the Seiberg-Witten equations lead to nontrivial estimates 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 on smooth compact 4-manifolds with a non-zero Seiberg-Witten invariant. These results considerably refine those previously obtained [21] by using...
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