Verfasst von:	Quintino, Áurea Casinhas [VerfasserIn]
Titel:	Constrained Willmore surfaces
Titelzusatz:	symmetries of a Möbius invariant integrable system
Verf.angabe:	Áurea Casinhas Quintino (NOVA University Lisbon)
Verlagsort:	Cambridge ; New York, NY ; Port Melbourne ; New Delhi ; Singapore
Verlag:	Cambridge University Press
Jahr:	2021
Umfang:	xiii, 246 Seiten
Gesamttitel/Reihe:	London Mathematical Society Lecture Note Series ; 465
Fussnoten:	Literaturverzeichnis: Seite 240-244
ISBN:	978-1-108-79442-8
Abstract:	"This work is dedicated to the study of the Möbius invariant class of constrained Willmore surfaces and its symmetries. Characterized by the perturbed harmonicity of the mean curvature sphere congruence, a generalization of the well-developed integrable systems theory of harmonic maps emerges. The starting point is a zero-curvature characterization, due to Burstall-Calderbank, which we derive from the underlying variational problem. Constrained Willmore surfaces come equipped with a family of flat metric connections. We then define a spectral deformation, by the action of a loop of flat metric connections; Bäcklund transformations, defined by the application of a version of the Terng-Uhlenbeck dressing action by simple factors; and, in 4-space, Darboux transformations, based on the solution of a Riccati equation, generalizing the transformation of Willmore surfaces presented in the quaternionic setting by Burstall-Ferus-Leschke-Pedit-Pinkall. We establish a permutability between spectral deformation and Bäcklund transformation and prove that non-trivial Darboux transformation of constrained Willmore surfaces in 4-space can be obtained as a particular case of Bäcklund transformation. All these transformations corresponding to the zero Lagrange multiplier preserve the class of Willmore surfaces. We verify that both spectral deformation and Bäcklund transformation preserve the class of constrained Willmore surfaces admitting 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, in the latter case. Constrained Willmore transformation proves to be unifying to the rich transformation theory of CMC surfaces in 3-space"--
DOI:	doi:10.1017/978-1-108-88547-8
URL:	Inhaltsverzeichnis: https://www.gbv.de/dms/tib-ub-hannover/173721122X.pdf
	zbMATH: https://zbmath.org/?q=an%3A7298516
	DOI: https://doi.org/10.1017/978-1-108-88547-8
Schlagwörter:	(s)Willmore-Fläche    / (s)Verallgemeinerung    / (s)Integrables System    / (s)Möbius-Transformation    / (s)Konstante mittlere Krümmung    / (s)Bäcklund-Transformation    / (s)Darboux-Transformation
Sprache:	eng
Bibliogr. Hinweis:	Erscheint auch als : Online-Ausgabe: Quintino, Áurea Casinhas, 1974 - : Constrained Willmore surfaces. - Cambridge, UK : Cambridge University Press, 2021. - 1 Online-Ressource (xiii, 246 pages)
RVK-Notation:	SK 370
K10plus-PPN:	173721122X
Verknüpfungen:	→ Übergeordnete Aufnahme