Alexander I. Bobenko Tu Berlin, Ulrich Eitner

Painleve Equations in the Differential Geometry of Surfaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. TOC:Introduction. Basics of Painlevé Equations.- Bonnet Surfaces in Euclidean Three-space.- Bonnet Surfaces S3 and H3 and Surfaces with Harmonic Inverse Mean Curvature.- Surfaces with Constant Curvature.- Appendices.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 120
• Erscheinungstermin: 1. Juli 2003
• Englisch
• ISBN-13: 9783540444527
• Artikelnr.: 53380764

Inhaltsangabe

1. Introduction.- 2. Basics on Painlevé Equations and Quaternionic Description of Surfaces.- 3. Bonnet Surfaces in Euclidean Three-space.- 4. Bonnet Surfaces in S3 and H3 and Surfaces with Harmonic Inverse Mean Curvature.- 5. Surfaces with Constant Curvature.- 6. Appendices.