Deformations of Scalar-Flat Anti-Self-Dual metrics and Quotients of Enriques Surfaces
Abstract
In this article, we prove that a quotient of a K3 surface by a free Z2+Z2 action does not admit any metric of positive scalar curvature. This shows that the scalar flat anti self-dual metrics (SF-ASD) on this manifold can not be obtained from a family of metrics for which the scalar curvature changes sign, contrary to the previously known constructions of this kind of metrics on manifolds of b+=0.
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