Constrained elastic curves and surfaces with spherical curvature lines

DOI10.1512/iumj.2023.72.9487arXiv2104.11058OpenAlexW3152592162MaRDI QIDQ6186733

Mason Pember, Joseph Cho, Gudrun Szewieczek

Publication date: 10 January 2024

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.11058

Mathematics Subject Classification ID

Foliations (differential geometric aspects) (53C12) Surfaces in Euclidean and related spaces (53A05) Local submanifolds (53B25) Geometric evolution equations (53E99)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lie geometry of linear Weingarten surfaces
• The total squared curvature of closed curves
• Deformation and applicability of surfaces in Lie sphere geometry
• Constrained Willmore surfaces
• Lie geometry of flat fronts in hyperbolic space
• Hopf tori in \(S^ 3\)
• Counterexample to a conjecture of H. Hopf
• Minimal tori in \(S^ 3\) whose lines of curvature lie in \(S^ 2\)
• Lie sphere geometry and integrable systems.
• Polynomial conserved quantities of Lie applicable surfaces
• Ribaucour transformations for constant mean curvature and linear Weingarten surfaces.
• Laguerre geometry of surfaces with plane lines of curvature
• Channel surfaces in Lie sphere geometry
• Lie applicable surfaces and curved flats
• Lie applicable surfaces
• The Ribaucour families of discrete R-congruences
• Constrained Willmore tori and elastic curves in 2-dimensional space forms
• Deformation of minimal surfaces with planar curvature lines
• The Ribaucour transformation in Lie sphere geometry
• Particles with curvature and torsion in three-dimensional pseudo-Riemannian space forms
• Constant negative Gaussian curvature tori and their singularities
• Non-special, non-canal isothermic tori with spherical lines of curvature
• INTEGRABLE SYSTEMS IN PROJECTIVE DIFFERENTIAL GEOMETRY
• Special isothermic surfaces of type d
• Curves in the Hyperbolic Plane and mean Curvature of Tori in 3-Space
• Constant mean curvature tori in terms of elliptic functions.
• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
• On Ribaucour transformations and applications to linear Weingarten surfaces
• ANALOG OF WILCZYNSKI'S PROJECTIVE FRAME IN LIE SPHERE GEOMETRY: LIE-APPLICABLE SURFACES AND COMMUTING SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS
• Non-Euclidean Laguerre Geometry and Incircular Nets
• Semi-discrete isothermic surfaces
• Explicit examples to the H-problem of Heinz Hopf

This page was built for publication: Constrained elastic curves and surfaces with spherical curvature lines