Discrete linear Weingarten surfaces. (English) Zbl 1411.53007
Authors’ abstract: Discrete linear Weingarten surfaces in space forms are characterized as special discrete \(\Omega\)-nets, a discrete analogue of Demoulin’s \(\Omega\)-surfaces. It is shown that the Lie-geometric deformation of \(\Omega\)-nets descends to a Lawson transformation for discrete linear Weingarten surfaces, which coincides with the well-known Lawson correspondence in the constant mean curvature case.
Reviewer: Victor Alexandrov (Novosibirsk)
MSC:
| 53A05 | Surfaces in Euclidean and related spaces |
| 52B70 | Polyhedral manifolds |
| 51K10 | Synthetic differential geometry |
| 52A39 | Mixed volumes and related topics in convex geometry |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53A40 | Other special differential geometries |
Keywords:
linear Weingarten net; affine projection; principal contact element net; Lie quadric; linear sphere; complex; Legendre lift; Legendre map; Ribaucour sphere congruences; isothermic sphere congruences; Lawson transformation; middle connectionReferences:
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