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. 
@article{INTO_2022_214_a8,
     author = {E. Yu. Kuzmina},
     title = {Hypersurfaces with constant principal curvatures in {Euclidean} space $V^{n+1}$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {76--81},
     publisher = {mathdoc},
     volume = {214},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_214_a8/}
}
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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/