Painleve III: A Case Study in the Geometry of Meromorphic Connections

Painleve III: A Case Study in the Geometry of Meromorphic Connections

AngličtinaEbook
Guest, Martin A.
Springer International Publishing
EAN: 9783319665269
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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, 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 <i> tt*</i> geometry and harmonic bundles. As an application, a new global picture o0 is given.
EAN 9783319665269
ISBN 331966526X
Typ produktu Ebook
Vydavateľ Springer International Publishing
Dátum vydania 14. októbra 2017
Jazyk English
Krajina Uruguay
Autori Guest, Martin A.; Hertling, Claus
Séria Lecture Notes in Mathematics