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

It is proved that conformal infinitesimal deformations of a surfaceF^kin Riemannian space, and they only, are areally recurrent infinitesimal deformations. All areally recurrent deformations of the hypersphereSⁿ–1 inEⁿ are described.Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 284–290, February, 1996.This research was partially supported by the Russian Foundation for Basic Research under grant No. 95-01-00228a.