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OverviewFrom 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. Full Product DetailsAuthor: Áurea Casinhas Quintino (Universidade Nova de Lisboa, Portugal)Publisher: Cambridge University Press Imprint: Cambridge University Press Dimensions: Width: 15.20cm , Height: 1.50cm , Length: 22.80cm Weight: 0.400kg ISBN: 9781108794428ISBN 10: 1108794424 Pages: 258 Publication Date: 10 June 2021 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsIntroduction; 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.ReviewsAuthor InformationÁurea 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. Tab Content 6Author Website:Countries AvailableAll regions |
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