Geodesic
On some second-order rigidity conditions for analytic surfaces
Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 233-242 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that an analytic surface does not admit a nontrivial analytic infinitesimal deformation of the second order satisfying one of the following conditions: a) preservation of the normal curvature of a planar closed convex curve belonging to the surface; b) each point of a closed curve belonging to the surface slides in a rectifiable curve. 
@article{MZM_1973_14_2_a8,
     author = {N. G. Perlova},
     title = {On some second-order rigidity conditions for analytic surfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {233--242},
     year = {1973},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a8/}
}
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N. G. Perlova. On some second-order rigidity conditions for analytic surfaces. Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 233-242. http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a8/