0 Ricci Curvature , Minimal Volumes , and Seiberg - Witten Theory Claude LeBrun
نویسنده
چکیده
We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manifold minimizes volume among all metrics satisfying a point-wise lower bound on sectional curvature plus suitable multiples of the scalar curvature. These estimates also imply new non-existence results for Einstein metrics.
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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