Overview

This book brings together two different branches of mathematics: the theory of Painleve 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 Painleve 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 Painleve equations: the theory of isomonodromic deformation and the Painleve 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 Painleve equations. Researchers working in one of these areas can become familiar with another relevant branch of mathematics.

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9783540414148

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