Geodesic
Curvature Properties of Some Class of Hypersurfaces in Euclidean Spaces
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 165

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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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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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