Publications de l'Institut Mathématique, Nouvelle Série Vol. 98(112), pp. 165–177 (2015) 

Curvature properties of some class of hypersurfaces in Euclidean spacesKatarzyna SawiczDepartment of Applied Mathematics, Karol Adamiecki University of Economics in Katowice, Katowice, PolandAbstract: We determine curvature properties of pseudosymmetry type of hypersurfaces in Euclidean spaces $\mathbb E^{n+1}$, $n\geqslant 5$, having three distinct nonzero principal curvatures $\lambda_1$, $\lambda_2$ and $\lambda_3$ of multiplicity $1$, $p$ and $np1$, 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. Keywords: Tachibana tensor; pseudosymmetry type curvature condition; hypersurface; principal curvature Classification (MSC2000): 53B20; 53B25; 53C25 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.
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