Painleve III: A Case Study in the Geometry of Meromorphic Connections (Paperback, 1st ed. 2017)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2198
Release date:	October 2017
First published:	2017
Authors:	Martin Guest • Claus Hertling
Dimensions:	235 x 155 x 17mm (L x W x T)
Format:	Paperback
Pages:	204
Edition:	1st ed. 2017
ISBN-13:	978-3-319-66525-2
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Promotions
LSN:	3-319-66525-1
Barcode:	9783319665252

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