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Hypersurfaces in spaces of constant curvature satisfying some Ricci-type equations

Katarzyna Sawicz — 2004

Colloquium Mathematicae

We investigate hypersurfaces M in semi-Riemannian spaces of constant curvature satisfying some Ricci-type equations and for which the tensor H³ is a linear combination of the tensor H², the second fundamental tensor H of M and the metric tensor g of M.

On some class of hypersurfaces with three distinct principal curvatures

Katarzyna Sawicz — 2005

Banach Center Publications

We investigate hypersurfaces M in spaces of constant curvature with some special minimal polynomial of the second fundamental tensor H of third degree. We present a curvature characterization of pseudosymmetry type for such hypersurfaces. We also prove that if such a hypersurface is a manifold with pseudosymmetric Weyl tensor then it must be pseudosymmetric.

On Curvature Characterizations of Some Hypersurfaces in Spaces of Constant Curvature

Katarzyna Sawicz — 2006

Publications de l'Institut Mathématique

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