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Spherical Monopoles and Holomorphic Functions
Author(s) -
Pauly Marc
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/33.1.83
Subject(s) - holomorphic function , geodesic , mathematics , magnetic monopole , pure mathematics , equivalence (formal languages) , metric (unit) , class (philosophy) , space (punctuation) , mathematical physics , mathematical analysis , physics , quantum mechanics , computer science , operations management , artificial intelligence , economics , operating system
We show that any gauge‐equivalence class of solutions (∇, Φ) of the monopole equation F ∇ = * d ∇ Φ, defined on an open set Ω of S 3 (equipped with its standard metric), induces canonically a holomorphic function on the complex 2‐dimensional space of all geodesics on S 3 entirely contained in Ω.