TU Berlin / Eitner Painleve Equations in the Differential Geometry of Surfaces

2000
ISBN: 978-3-540-44452-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1753, 120 Seiten, eBook

Reihe: Lecture Notes in Mathematics

Zielgruppe

Research

Autoren/Hrsg.

TU Berlin, Alexander I. Bobenko

Eitner, Ulrich

Inhaltsverzeichnis

1. Introduction 2. Basics of Painlevé Equations and Quaternionic Description of Surfaces
2.1. Painlevé Property and Painlevé Equations
2.2. 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