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Painleve III: A Case Study in the Geometry of Meromorphic Connections (Paperback, 1st ed. 2017)
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Painleve III: A Case Study in the Geometry of Meromorphic Connections (Paperback, 1st ed. 2017)
Series: Lecture Notes in Mathematics, 2198
Expected to ship within 10 - 15 working days
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The purpose of this monograph is two-fold: it introduces a
conceptual language for the geometrical objects underlying Painleve
equations, and it offers new results on a particular Painleve III
equation of type PIII (D6), called PIII (0, 0, 4, 4), describing
its relation to isomonodromic families of vector bundles on P1 with
meromorphic connections. This equation is equivalent to the radial
sine (or sinh) Gordon equation and, as such, it appears widely in
geometry and physics. It is used here as a very concrete and
classical illustration of the modern theory of vector bundles with
meromorphic connections. Complex multi-valued solutions on C* are
the natural context for most of the monograph, but in the last four
chapters real solutions on R>0 (with or without singularities)
are addressed. These provide examples of variations of TERP
structures, which are related to tt geometry and harmonic bundles.
As an application, a new global picture o0 is given.
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