Geodesic
On infinitesimal bendings of troughs of revolution. I
Sbornik. Mathematics, Tome 27 (1975) no. 1, pp. 103-117 
I. Kh. Sabitov. On infinitesimal bendings of troughs of revolution. I. Sbornik. Mathematics, Tome 27 (1975) no. 1, pp. 103-117. http://geodesic.mathdoc.fr/item/SM_1975_27_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a trough of revolution possesses second-order rigidity with respect to $C^1$-smooth infinitesimal bendings. A necessary and sufficient condition is given for the existence of infinitesimal first-order bendings. Bibliography: 3 titles.

[1] N. G. Perlova, I. Kh. Sabitov, “Zhestkost vtorogo poryadka zhelobov vrascheniya klassa $C^2$”, Vestnik MGU, Seriya matem. mekh., 1975, no. 5 | MR

[2] T. Minagawa, T. Rado, “On the infinitesimal rigidity of surfaces of revolution”, Math. Z., 59 (1953), 151–163 | DOI | MR | Zbl

[3] A. V. Pogorelov, Vneshnyaya geometriya vypuklykh poverkhnostei, izd-vo «Nauka», Moskva, 1969 | MR