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Quasi-Einstein hypersurfaces in semi-Riemannian space forms

Ryszard Deszcz, Marian Hotloś, Zerrin Sentürk (2001)

Colloquium Mathematicae

We investigate curvature properties of hypersurfaces of a semi-Riemannian space form satisfying R·C = LQ(S,C), which is a curvature condition of pseudosymmetry type. We prove that under some additional assumptions the ambient space of such hypersurfaces must be semi-Euclidean and that they are quasi-Einstein Ricci-semisymmetric manifolds.

Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

Georgi Ganchev, Velichka Milousheva (2014)

Open Mathematics

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all rotational quasi-minimal surfaces of elliptic, hyperbolic and parabolic type, respectively.

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