Publisher's Synopsis
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.
