A property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space

It is proved that conformal infinitesimal deformations of a surface $F^k$ in Riemannian space, and they only, are areally recurrent infinitesimal deformations. All areally recurrent deformations of the hypersphere $S^{n-1}$ in $E^n$ are described.