Geodesic
On infinitesimal bendings of troughs of revolution.~II
Sbornik. Mathematics, Tome 28 (1976) no. 1, pp. 41-48

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It is shown that if a trough of revolution $S\in C^1$ does not admit $C^1$ infinitesimal bendings with the parabolic parallel fixed, then $S$ possesses second-order $C^1$-rigidity, and the existence of first-order bendings is determined by a certain effectively verifiable necessary and sufficient condition on the meridian. Bibliography: 4 titles. 
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     author = {I. Kh. Sabitov},
     title = {On infinitesimal bendings of troughs of {revolution.~II}},
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I. Kh. Sabitov. On infinitesimal bendings of troughs of revolution.~II. Sbornik. Mathematics, Tome 28 (1976) no. 1, pp. 41-48. http://geodesic.mathdoc.fr/item/SM_1976_28_1_a2/