Infinitesimal bendings of a class of multidimensional surfaces with boundary

Infinitesimal bendings are considered for a $2k$-dimensional ($k\geqslant1$) surface of class $C^2$ with boundary in $3k$-dimensional Euclidean space in the case when the surface is star-shaped with respect to some $(k-1)$-dimensional plane or projects in a one-to-one manner on some $2k$-dimensional plane. Tests are established for the rigidity of such surfaces under boundary conditions of sliding.
Bibliography: 12 titles.