Karstoft, Henrik Conformal imbeddings of the complex projective plane and self-dual connections. (English) Zbl 0760.57009 Math. Scand. 70, No. 2, 207-226 (1992). 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.) Keywords:self-dual connection on a complex analytic surface; conformal imbeddings of the complex projective plane into the quaternion projective plane; moduli space of one-instantons; conformal maps into quaternion projective space PDFBibTeX XMLCite \textit{H. Karstoft}, Math. Scand. 70, No. 2, 207--226 (1992; Zbl 0760.57009) Full Text: DOI EuDML