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- catalog abstract "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.".
- catalog contributor b11965136.
- catalog contributor b11965137.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog description "Includes bibliographical references (p. [113]-117) and index.".
- catalog description "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.".
- catalog 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.".
- catalog extent "vi, 120 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540414142 (softcover : acid-free paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1753.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1753".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 515/.352 21".
- catalog subject "Global analysis (Mathematics)".
- catalog subject "Global differential geometry.".
- catalog subject "Mathematical physics.".
- catalog subject "Mathematics.".
- catalog subject "Painlevé equations.".
- catalog subject "QA3 .L28 no. 1753 QA649".
- catalog subject "Surfaces.".
- catalog tableOfContents "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.".
- catalog title "Painlevé equations in the differential geometry of surfaces / Alexander I. Bobenko, Ulrich Eitner.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".