Constrained Willmore Surfaces - Symmetries of a Mobius Invariant Integrable System

From Bäcklund to Darboux: a comprehensive journey through the transformation theory of constrained Willmore surfaces, with applications to constant mean curvature surfaces.

List of contents

Introduction; 1. A bundle approach to conformal surfaces in space-forms; 2. The mean curvature sphere congruence; 3. Surfaces under change of flat metric connection; 4. Willmore surfaces; 5. The Euler-Lagrange constrained Willmore surface equation; 6. Transformations of generalized harmonic bundles and constrained Willmore surfaces; 7. Constrained Willmore surfaces with a conserved quantity; 8. Constrained Willmore surfaces and the isothermic surface condition; 9. The special case of surfaces in 4-space; Appendix A. Hopf differential and umbilics; Appendix B. Twisted vs. untwisted Bäcklund transformation parameters; References; Index.

About the author

Áurea Casinhas Quintino is an Assistant Professor at NOVA University Lisbon and a member of CMAFcIO – Center for Mathematics, Fundamental Applications and Operations Research, Faculty of Sciences of the University of Lisbon. Her research interests focus on integrable systems in Riemannian geometry.

Summary

This monograph presents the transformation theory of Willmore surfaces (possibly with a constraint), including applications to surfaces of constant mean curvature. Self-contained accounts of the core topics make it suitable for newcomers to the field, while many detailed computations and new results make it an appealing reference for experts.

Product details

• Authors: Aurea Casinhas Quintino, Áurea Casinhas Quintino, Aurea Casinhas (Universidade Nova De Lis Quintino, Aurea Casinhas (Universidade Nova de Lisboa Quintino
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 30.04.2021
• EAN: 9781108794428
• ISBN: 978-1-108-79442-8
• No. of pages: 258
• Series: London Mathematical Society Lecture Note Series; London Mathematical Society Le
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > General, dictionaries; SCIENCE / Physics / Mathematical & Computational, MATHEMATICS / Geometry / Differential, Mathematical physics, Differential & Riemannian geometry, Differential and Riemannian geometry, Mathematical / Computational / Theoretical physics