Constrained Willmore Surfaces

Symmetries of a Möbius Invariant Integrable System

By:

Aurea Casinhas Quintino

Format:

Paperback / softback

Series:

London Mathematical Society Lecture Note Series,

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Description

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.

Author Biography:

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.

Release date Australia

June 10th, 2021

Author

Aurea Casinhas Quintino

Audience

Professional & Vocational

Illustrations

Worked examples or Exercises

Pages

258

Series

London Mathematical Society Lecture Note Series,

Dimensions

152x228x15

ISBN-13

9781108794428

Product ID

33887322

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