Geodesic
A characteristic feature of the~$n$-dimensional sphere in the~Euclidean space $E^{n+p}$
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 315-320

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Submanifolds with zero geodesic torsion in Euclidean space are studied. Conditions are found under which submanifolds of this class are hyperspheres of certain Euclidean spaces of lower dimension 
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     author = {I. I. Bodrenko},
     title = {A characteristic feature of the~$n$-dimensional sphere in {the~Euclidean} space $E^{n+p}$},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_83_2_a1/}
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I. I. Bodrenko. A characteristic feature of the~$n$-dimensional sphere in the~Euclidean space $E^{n+p}$. Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 315-320. http://geodesic.mathdoc.fr/item/SM_1995_83_2_a1/