# Hypersurfaces satisfying pseudo-symmetry conditions for their weyl conformal curvature tensor

Deprez, J. and Deszcz, R. and Verstraelen, L. and Yaprak, Sahnur (1995) Hypersurfaces satisfying pseudo-symmetry conditions for their weyl conformal curvature tensor. Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., LXXIII. pp. 165-181.

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atti_3_1995_165.pdf - Submitted Version

We study the hypersurfaces of Euclidean space $E^n^+^1$ satisfying the condition $C\cdot\ C=fQ(g,C)$. We prove that all hypersurfaces with at most three distinct principal curvatures with multiplicities, 1, 1 and n-2 satisfy this condition. We also examine the condition $C\cdot\ R=fQ(g,R)$. We show that a hypersurface M satisfy this condition if and only if M has at most two distinct principal curvatures or the type number of M is two.