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Infinitesimal deformations of higher order of multi-dimensional surfaces in spaces of constant curvature. (Russian) Zbl 0629.53020
A system of equations for the variation of the coefficients of the second fundamental form and the torsion forms of an n-dimensional submanifold F in an m-dimensional space W of constant curvature K obtained from the r- fold variation of the equations of Gauss, Codazzi and Ricci is considered. It is shown that to every solution of this system there corresponds only one infinitesimal bending of F of order r in W. Using these results the author studies the infinitesimal bendings and the analytical bendings of order r of a special class of submanifolds in a flat space.
Reviewer: St.Hineva

MSC:
53B25 Local submanifolds
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