On the Riemannian Geometry of Seiberg-witten Moduli Spaces
نویسنده
چکیده
We construct a natural L-metric on the perturbed Seiberg-Witten moduli spaces Mμ+ of a compact 4-manifold M , and we study the resulting Riemannian geometry of Mμ+ . We derive a formula which expresses the sectional curvature of Mμ+ in terms of the Green operators of the deformation complex of the Seiberg-Witten equations. In case M is simply connected, we construct a Riemannian metric on the Seiberg-Witten principal U(1) bundle P → Mμ+ such that the bundle projection becomes a Riemannian submersion. On a Kähler surface M , the L-metric on Mμ+ coincides with the natural Kähler metric on moduli spaces of vortices.
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