Abstract
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 hypersphereS n−1 inE n are described.
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References
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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.
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Fomenko, V.T. A property of conformal infinitesimal deformations of multidimensional surfaces in Riemannian space. Math Notes 59, 201–204 (1996). https://doi.org/10.1007/BF02310961
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DOI: https://doi.org/10.1007/BF02310961