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Conformal imbeddings of the complex projective plane and self-dual connections. (English) Zbl 0760.57009

We show that there is a relation between self-dual connection on a complex analytic surface \(X\) and certain conformal maps from \(X\) into quaternion projective space. This is used to construct a non-trivial set of conformal imbeddings of the complex projective plane into the quaternion projective plane. We also present a construction of the moduli space of one-instantons on the complex projective plane, as a double coset space of the general quaternion linear group of rank 3.
Reviewer: H.Karstoft

MSC:

57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
58D27 Moduli problems for differential geometric structures
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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