Deformation and applicability of surfaces in Lie sphere geometry

DOI10.2748/tmj/1156256399zbMath1155.53306arXivmath/0408009OpenAlexW1967137796MaRDI QIDQ854466

Lorenzo Nicolodi, Emilio Musso

Publication date: 4 December 2006

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408009

zbMATH Keywords

rigidityLie sphere geometrydeformation of surfacesLegendre surfacesLie-applicable surfaces

Mathematics Subject Classification ID

Rigidity results (53C24) Other special differential geometries (53A40)

Related Items (11)

Lie applicable surfaces and curved flats ⋮ Holomorphic differentials and Laguerre deformation of surfaces ⋮ \(G\)-deformations of maps into projective space ⋮ Discrete Ω$\Omega$‐nets and Guichard nets via discrete Koenigs nets ⋮ Lie geometry of linear Weingarten surfaces ⋮ Constrained elastic curves and surfaces with spherical curvature lines ⋮ Polynomial conserved quantities of Lie applicable surfaces ⋮ Laguerre isoparametric and Dupin hypersurfaces in \(\mathbb {R}^n\) ⋮ Channel surfaces in Lie sphere geometry ⋮ Lie geometry of flat fronts in hyperbolic space ⋮ DISCRETE LINEAR WEINGARTEN SURFACES

Cites Work

• Dupin hypersurfaces
• Deformation of submanifolds of homogeneous spaces
• On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry
• Lie sphere geometry and integrable systems.
• Laguerre geometry of surfaces with plane lines of curvature
• Non-special, non-canal isothermic tori with spherical lines of curvature
• INTEGRABLE SYSTEMS IN PROJECTIVE DIFFERENTIAL GEOMETRY
• THE BIANCHI–DARBOUX TRANSFORM OF L-ISOTHERMIC SURFACES
• ANALOG OF WILCZYNSKI'S PROJECTIVE FRAME IN LIE SPHERE GEOMETRY: LIE-APPLICABLE SURFACES AND COMMUTING SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS
• Lie sphere geometry. With applications to submanifolds
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