ENGLISH

Painlevé Equations in the Differential Geometry of Surfaces

By Alexander I. Bobenko , Ulrich Eitner (eds.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2000
ISBN
978-3-540-41414-8, 978-3-540-44452-7
DOI
10.1007/b76883
Language
english
Format
PDF
Filesize
3 MB (2908633 bytes)
Series
Lecture Notes in Mathematics 1753
Edition
1
Pages
120\124
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Differential Geometry;Global Analysis and Analysis

Description

This book brings together two different branches of mathematics: the theory of Painlevé and the theory of surfaces. Self-contained introductions to both these fields are presented. It is shown how some classical problems in surface theory can be solved using the modern theory of Painlevé equations. In particular, an essential part of the book is devoted to Bonnet surfaces, i.e. to surfaces possessing families of isometries preserving the mean curvature function. A global classification of Bonnet surfaces is given using both ingredients of the theory of Painlevé equations: the theory of isomonodromic deformation and the Painlevé property. The book is illustrated by plots of surfaces. It is intended to be used by mathematicians and graduate students interested in differential geometry and Painlevé equations. Researchers working in one of these areas can become familiar with another relevant branch of mathematics.

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