Trapezoidal discrete surfaces: geometry and integrability. (English) Zbl 0941.53007
The authors study trapezoidal surfaces, i.e., surfaces composed of trapezoidal quadrilaterals (discrete analogues of surfaces of revolution). They define discrete principal curvatures and prove that the discrete Gauss equation is the discrete Schrödinger equation. In particular, the authors define discrete surfaces of revolution and investigate surfaces of constant Gaussian curvature, their Darboux transforms, and the class of discrete Weingarten surfaces of revolution for which the principal curvatures are proportional.
Reviewer: Vladislav V.Goldberg (Newark/New Jersey)
MSC:
| 53A05 | Surfaces in Euclidean and related spaces |
| 37K25 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry |
| 39A12 | Discrete version of topics in analysis |
Keywords:
trapezoidal discrete surface; surface of revolution; principal curvature; Gauss equation; discrete Schrödinger equation; Darboux transformReferences:
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