Painlevé equations in the differential geometry of surfaces /
This book brings together two different branches of mathematics: the theory of Painlev 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 Painlev equations. In...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[2000]
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1753. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | This book brings together two different branches of mathematics: the theory of Painlev 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 Painlev 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 Painlev equations: the theory of isomonodromic deformation and the Painlev 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 Painlev equations. Researchers working in one of these areas can become familiar with another relevant branch of mathematics. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (vi, 120 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages [113]-117) and index. |
| ISBN: | 9783540444527 (electronic bk.) 3540444521 (electronic bk.) |
| ISSN: | 0075-8434 ; |