Abstract
The classical description of the structure of developable surfaces of torse type is formally possible only starting with C 3-smoothness. We consider developable surfaces of class C 2 and show that the directions of their generators at the boundary points of a surface belong to the tangent cone of the boundary curve. In analytical terms we give a necessary and sufficient condition for C 1-smooth surfaces with locally Euclidean metric to belong to the class of the so-called normal developable surfaces introduced by Burago and Shefel’.
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To Yuriĭ Grigor’evich Reshetnyak in token of sincere respect.
Original Russian Text Copyright © 2009 Sabitov I. Kh.
The author was partially supported by the Ministry for Science and Education of the Russian Federation (Grant RNP 2.1.1.3704) and the Russian Foundation for Basic Research (Grant 01-09-00179).
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Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 5, pp. 1163–1175, September–October, 2009.
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Sabitov, I.K. On the developable ruled surfaces of low smoothness. Sib Math J 50, 919–928 (2009). https://doi.org/10.1007/s11202-009-0102-8
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DOI: https://doi.org/10.1007/s11202-009-0102-8