Spherical Monopoles and Holomorphic Functions
Copyright policy )Spherical Monopoles and Holomorphic Functions
In a monopole \((\nabla,\Phi)\) the curvature \(F_\nabla\) and the covariant derivative of the section \(\Phi\) are related by a nonlinear first-order partial differential equation \(F_\nabla= *d_\nabla\Phi\), where \(*\) is the Hodge star [see \textit{M. F. Atiyah, N. J. Hitchin} and \textit{I. M. Singer}, Proc. R. Soc. Lond., Ser. A 362, 425--461 (1978; Zbl 0389.53011); the author, Math. Ann. 311, 125--146 (1998; Zbl 0920.58011)]. It is shown that any gauge-equivalence class of solutions on an open set \(\Omega\) of \(S^3\) induces canonically a twistor object, namely a holomorphic function \(h_{(\nabla,\Phi)}\) on the complex two-dimensional space of all geodesics on \(S^3\) contained in \(\Omega\).
- Paris 13 University France
- University of Paris France
spherical monopole, Twistor methods in differential geometry, twistor, Moduli problems for differential geometric structures, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
spherical monopole, Twistor methods in differential geometry, twistor, Moduli problems for differential geometric structures, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!