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

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Curvature properties of some class of hypersurfaces in Euclidean spaces

Katarzyna Sawicz

Department of Applied Mathematics, Karol Adamiecki University of Economics in Katowice, Katowice, Poland

Abstract: 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.

Keywords: Tachibana tensor; pseudosymmetry type curvature condition; hypersurface; principal curvature

Classification (MSC2000): 53B20; 53B25; 53C25

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Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.

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