Geodesic
On infinitesimal deformations of surfaces of positive curvature with an isolated flat point
Sbornik. Mathematics, Tome 12 (1970) no. 4, pp. 595-614 
Z. D. Usmanov. On infinitesimal deformations of surfaces of positive curvature with an isolated flat point. Sbornik. Mathematics, Tome 12 (1970) no. 4, pp. 595-614. http://geodesic.mathdoc.fr/item/SM_1970_12_4_a7/
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     title = {On~infinitesimal deformations of surfaces of positive curvature with an isolated flat point},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study infinitesimal deformations of convex pieces of surfaces with boundary. It is assumed that the surface has positive gaussian curvature $K>0$. We investigate infinitesimal deformations, subject on the boundary of the surface to the condition $\lambda\delta k_n+\mu\delta\tau_g=\sigma$, where $\delta k_n$ and $\sigma\tau_g$ are variations of the normal curvature and geodesic torsion of the boundary, $\lambda$ and $\mu$ are fixed known functions, and $\sigma$ an arbitrary given function. We establish necessary and sufficient conditions for the rigidity of the surface under these boundary conditions. Bibliography: 12 titles.

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