Fedchenko Yu. S.
Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1396-1402
We study special infinitesimal geodesic deformations of the surfaces of revolution in the Euclidean space $E^3$.
Ukr. Mat. Zh. - 2003. - 55, № 12. - pp. 1697-1703
We present a variational generalization of the problem of infinitesimal geodesic deformations of surfaces in the Euclidean space E 3. By virtue of rotary deformation, the image of every geodesic curve is an isoperimetric extremal of rotation (in the principal approximation). The results are associated in detail with rotary-conformal deformations. The application of these results to the mechanics of elastic shells is given.