Almost-Kahler Anti-Self-Dual Metrics

2015/11/24 by Inyoung Kim, Kim, Inyoung · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1511.07656

openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the existence of strictly almost-Kahler anti-self-dual metrics on certain 4-manifolds by deforming scalar-flat Kahler metrics. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of Seiberg-Witten theory. In the process, we provide a simple new proof of the fact that any almost-Kahler anti-self-dual 4-manifold must have a non-trivial Seiberg-Witten invariant.

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• Product twistor spaces and Weyl geometry

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