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 
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/
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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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