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Piecewise smooth developable surfaces. (English. Russian original) Zbl 1180.53005
Proc. Steklov Inst. Math. 263, 214-235 (2008); translation from Tr. Mat. Inst. Steklova 263, 227-250 (2008).
The first half of the paper is a detailed discussion of developable surfaces in Euclidean 3-space. A developable surface with an edge of regression cannot be mapped isometrically into the plane because the points on the edge of regression do not have neighborhoods isometric to Euclidean disks. Here pieces of developable surfaces are considered which are smooth except along an edge where every point has a neighborhood isometric to a Euclidean disk. The main result of this paper is the following: In general, one part of such a surface which is bounded by the edge uniquely determines the other part.

MSC:
53A05 Surfaces in Euclidean and related spaces
52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
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