Geodesic
Hypersurfaces with constant principal curvatures in Euclidean space $V^{n+1}$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 214 (2022), pp. 76-81.

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Hypersurfaces in $E^{n+1}$ for which a thin fan is found are considered. It is shown that it exists only for hypersurfaces in $E^{n+1}$ with constant or proportional principal curvatures that differ from each other. The conditions for the existence of hypersurfaces in the Euclidean space $V^{n+1}$, whose main curvatures are constant (assuming that all the main curvatures are different from each other), are clarified.
Mots-clés : $G$-structures
Keywords: differentiable manifold, structural function, thin fan, initial pair. 
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E. Yu. Kuzmina. Hypersurfaces with constant principal curvatures in Euclidean space $V^{n+1}$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 214 (2022), pp. 76-81. http://geodesic.mathdoc.fr/item/INTO_2022_214_a8/

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