Constrained Willmore Surfaces: Symmetries of a Möbius Invariant Integrable System

From B cklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, B cklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed computations and new results unavailable elsewhere in the literature make it also an appealing reference for experts.

Author: Áurea Casinhas Quintino
Publisher: Cambridge University Press
Published: 08/05/2021
Pages: 258
Binding Type: Paperback
Weight: 0.90lbs
Size: 8.90h x 7.70w x 0.50d
ISBN: 9781108794428

About the Author
Quintino, Áurea Casinhas: - "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."