Constrained Willmore Surfaces: Symmetries of a Möbius Invariant Integrable System

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Áurea Casinhas Quintino (Universidade Nova de Lisboa, Portugal)

Constrained Willmore Surfaces

Symmetries of a Möbius Invariant Integrable System

Áurea Casinhas Quintino (Universidade Nova de Lisboa, Portugal)

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English

Cambridge University Press
10 June 2021

Differential & Riemannian geometry; Mathematical physics

Series: London Mathematical Society Lecture Note Series

From Bäcklund 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, Bäcklund 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.

By: Áurea Casinhas Quintino (Universidade Nova de Lisboa Portugal)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 228mm, Width: 152mm, Spine: 15mm
Weight: 400g
ISBN: 9781108794428
ISBN 10: 1108794424
Series: London Mathematical Society Lecture Note Series
Pages: 258
Publication Date: 10 June 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.