Geodesic
Curvature Properties of Some Class of Hypersurfaces in Euclidean Spaces
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 165 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We determine curvature properties of pseudosymmetry type of hypersurfaces in Euclidean spaces $\mathbb E^{n+1}$, $n\geqslant 5$, having three distinct non-zero principal curvatures $\lambda_1$, $\lambda_2$ and $\lambda_3$ of multiplicity $1$, $p$ and $n-p-1$, respectively. For some hypersurfaces having this property the sum of $\lambda_1$, $\lambda_2$ and $\lambda_3$ is equal to the trace of the shape operator of $M$. We present an example of such hypersurface.
DOI : 10.2298/PIM141025001S
Classification : 53B20, 53B25 53C25
Keywords: Tachibana tensor, pseudosymmetry type curvature condition, hypersurface, principal curvature 
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     author = {Katarzyna Sawicz},
     title = {Curvature {Properties} of {Some} {Class} of {Hypersurfaces} in {Euclidean} {Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {165 },
     year = {2015},
     volume = {_N_S_98},
     number = {112},
     doi = {10.2298/PIM141025001S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM141025001S/}
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Katarzyna Sawicz. Curvature Properties of Some Class of Hypersurfaces in Euclidean Spaces. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 165 . doi: 10.2298/PIM141025001S

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