Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory
Differential Geometry
2007-05-23 v2 Algebraic Geometry
Geometric Topology
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.
Keywords
Cite
@article{arxiv.math/9803093,
title = {Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory},
author = {Claude LeBrun},
journal= {arXiv preprint arXiv:math/9803093},
year = {2007}
}
Comments
17 pages. LaTeX2e. Revised version improves estimates, simplifies proofs, and gives cleaner applications