A variational problem for surfaces in Laguerre geometry

DOI10.1090/S0002-9947-96-01698-4zbMath0864.58017OpenAlexW1632900689MaRDI QIDQ3837642

Emilio Musso, Lorenzo Nicolodi

Publication date: 10 December 1996

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01698-4

zbMATH Keywords

Laguerre geometryLegendre surfaces\(L\)-minimal surfaces

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Surfaces in Euclidean and related spaces (53A05) Other special differential geometries (53A40)

Related Items (24)

THE BIANCHI–DARBOUX TRANSFORM OF L-ISOTHERMIC SURFACES ⋮ Holomorphic differentials and Laguerre deformation of surfaces ⋮ Laguerre homogeneous surfaces in \(\mathbb R^3\) ⋮ Laguerre geometry of hypersurfaces in \({\mathbb R}^n\) ⋮ The second variational formula for Laguerre minimal hypersurfaces in \(\mathbb R^n\) ⋮ Möbius curvature, Laguerre curvature and Dupin hypersurface ⋮ Laguerre isothermic surfaces in \(\mathbb R^3\) and their Darboux transformation ⋮ Laguerre isoparametric hypersurfaces in \(\mathbb R^n\) with two distinct non-zero principal curvatures ⋮ Ruled Laguerre minimal surfaces ⋮ Laguerre geometry of surfaces with plane lines of curvature ⋮ Polynomial conserved quantities of Lie applicable surfaces ⋮ Hypersurfaces with parallel para‐Laguerre tensor in ⋮ Laguerre isoparametric and Dupin hypersurfaces in \(\mathbb {R}^n\) ⋮ Generalized Weingarten surfaces of harmonic type in hyperbolic 3-space ⋮ Laguerre minimal surfaces in \(\mathbb R^{3}\) ⋮ Classification of hypersurfaces with parallel Laguerre second fundamental form in \(\mathbb R^n\) ⋮ Complete Laguerre minimal surfaces in \(\mathbb R^3\) ⋮ Area preserving transformations in two-dimensional space forms and classical differential geometry ⋮ Edge offset meshes in Laguerre geometry ⋮ Laguerre geometry of surfaces in \(\mathbb R^3\) ⋮ Laguerre minimal surfaces, isotropic geometry and linear elasticity ⋮ Classification of Laguerre isoparametric hypersurfaces in R6 ⋮ Generalized spherical type hypersurfaces ⋮ On the Cauchy problem for the integrable system of Lie minimal surfaces

Cites Work

• A duality theorem for Willmore surfaces
• 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
• Harmonic Maps and Classical Surface Theory in Minkowski 3-Space
• Lie sphere geometry. With applications to submanifolds
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