This monograph presents the transformation theory of Willmore surfaces (possibly with a constraint), including applications to surfaces of constant mean curvature. Self-contained accounts of the core topics make it suitable for newcomers to the field, while many detailed computations and new results make it an appealing reference for experts.
This monograph presents the transformation theory of Willmore surfaces (possibly with a constraint), including applications to surfaces of constant mean curvature. Self-contained accounts of the core topics make it suitable for newcomers to the field, while many detailed computations and new results make it an appealing reference for experts.
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.
Inhaltsangabe
Introduction 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.
Introduction 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.
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