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Painleve Equations in the Differential Geometry of Surfaces : Lecture Notes in Mathematics - Alexander I. Bobenko

Painleve Equations in the Differential Geometry of Surfaces

Lecture Notes in Mathematics

Paperback Published: December 2000
ISBN: 9783540414148
Number Of Pages: 120

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1. Introduction 2. Basics of Painlevè Equations and Quaternionic Description of Surfaces2.1. Painlevè Property and Painlevè Equations2.2. Isomonodromic Deformations 2.3. Conformally Parametrized Surfaces 2.4. Quaternionic Description of Surfaces 3. Bonnet Surfaces in Euclidean three-space 3.1. Definition of Bonnet Surfaces and Simplest Properties 3.2. Local Theory away from Critical Points 3.3. Local Theory at Critical Points 3.4. Bonnet Surfaces via Painlev Transcendents 3.5. Global Properties of Bonnet Surfaces 3.6. Examples of Bonnet Surfaces 3.7. Schlesinger Transformations for Bonnet Surfaces 4. Bonnet Surfaces in S and H and Surfaces with Harmonic Inverse Mean Curvature 4.1. Surfaces in S3 and H3 4.2. Definition and Simplest Properties 4.3. Bonnet Surfaces in S3 and H3 away from Critical Points 4.4. Local Theory of Bonnet Surfaces in S and H at Critical Points 4.5. Bonnet Surfaces in S3 and H3 in Terms of Painlev Transcendents 4.6. Global Properties of Bonnet Surfaces in Space Forms 4.7. Surfaces with Harmonic Inverse Mean Curvature 4.8. Bonnet Pairs of HIMC Surfaces 4.9. HIMC Bonnet Pairs in Painlev Transcendents 4.10. Examples of HIMC Surfaces 5. Surfaces with Constant Curvature 5.1. Surfaces with Constant Negative Gaussian Curvature and Two Straight Asymptotic Lines 5.2. Smyth Surfaces 5.3. Affine Spheres with Affine Straight Lines 6. Appendices

Introductionp. 1
Basics on Painleve Equations and Quaternionic Description of Surfacesp. 7
Bonnet Surfaces in Euclidean Three-spacep. 21
Bonnet Surfaces in S[superscript 3] and H[superscript 3] and Surfaces with Harmonic Inverse Mean Curvaturep. 65
Surfaces with Constant Curvaturep. 89
Appendicesp. 109
Referencesp. 112
Indexp. 119
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540414148
ISBN-10: 3540414142
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 120
Published: December 2000
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.69
Weight (kg): 0.19

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