Geodesic
Infinitesimal first- and second-order deformations of ribbed surfaces of revolution, preserving the normal curvature or geodesic torsion of the boundary parallel
Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 135-144

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Infinitesimal deformations of ribbed surfaces of revolution $S_n$ with preservation of the normal curvature $(A)$ or geodesic torsion $(B)$ of the boundary parallel are investigated. The following are proved: a convex surface $S_n$ is rigid under deformations $(A)$ and $(B)$; there are nonconvex surfaces $S_n$ that are nonrigid under deformations $(A)$ and $(B)$; any surface $S_n$ has second-order rigidity under deformations $(A)$; a surface $S_n$ that is nonrigid under these deformations. 
@article{MZM_1971_10_2_a2,
     author = {N. G. Perlova},
     title = {Infinitesimal first- and second-order deformations of ribbed surfaces of revolution, preserving the normal curvature or geodesic torsion of the boundary parallel},
     journal = {Matemati\v{c}eskie zametki},
     pages = {135--144},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a2/}
}
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N. G. Perlova. Infinitesimal first- and second-order deformations of ribbed surfaces of revolution, preserving the normal curvature or geodesic torsion of the boundary parallel. Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 135-144. http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a2/