Manifolds with an SU(2)-action on the tangent bundle

2003/09/18 by Roger Bielawski, Bielawski, Roger
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.math/0309301

23 pages

openalex publication_date 2003/09/18 · arxiv created 2003/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study manifolds arising as spaces of sections of complex manifolds fibering over the projective line with normal bundle of each section isomorphic to several copies of O(k). Such manifolds provide a natural setting for certain integrable systems, "monopoles", which comprise the Bogomolny hierarchy and the self-dual hierarchy.

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