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Explicit construction of self-dual 4-manifolds. (English) Zbl 0855.57028
A self-dual metric or conformal structure on a 4-manifold $$M$$ is a Riemannian metric $$g$$ or conformal class $$[g]$$ for which the Weyl conformal curvature tensor $$W$$ is self-dual; $$M$$ is then called a self-dual 4-manifold. Compact self-dual 4-manifolds have been extensively studied, and it is known that very many compact 4-manifolds do admit families of self-dual metrics, but explicit examples of self-dual metrics that can be written down in coordinates are comparatively few. In this paper we provide a geometrical framework within which it is possible to construct self-dual structures by solving a linear rather than a nonlinear equation, and use it to construct some new explicit examples of compact self-dual 4-manifolds.

##### MSC:
 57R57 Applications of global analysis to structures on manifolds 57N13 Topology of the Euclidean $$4$$-space, $$4$$-manifolds (MSC2010)
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