Geodesic
Hypersurfaces with proportional principal curvatures in $(n+1)$-dimensional Euclidean space
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 109-114

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In this paper, we find conditions of the existence of hypersurfaces in the $(n+1)$-dimensional Euclidean space $E^{n+1}$ whose main curvatures are proportional.
Mots-clés : $G$-structure
Keywords: differentiable manifold, structural function, thin fan, initial pair. 
@article{INTO_2023_224_a12,
     author = {E. Yu. Kuzmina},
     title = {Hypersurfaces with proportional principal curvatures in $(n+1)$-dimensional {Euclidean} space},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {109--114},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a12/}
}
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E. Yu. Kuzmina. Hypersurfaces with proportional principal curvatures in $(n+1)$-dimensional Euclidean space. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 109-114. http://geodesic.mathdoc.fr/item/INTO_2023_224_a12/