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On Ricci-pseudosymmetric hypersurfaces in space forms

Deszcz R., Hotloś M., Şentürk Z.

Demonstratio Mathematica

2004

Vol. 37, nr 1

203--214

We investigate curvature properties of hypersurfaces in semi-Riemannian space forms satisfying some curvature condition of pseudosymmetry type. Our main result states that such hypersurfaces must be Ricci-pseudosymmetric.

On some pseudosymmetry type hypersurfaces of semi-Euclidean spaces

Arslan K., Deszcz R., Ezentas R., Murathan C., Özgür C.

Demonstratio Mathematica

2003

Vol. 36, nr 4

971--984

We consider hypersurfaces of a semi-Euclidean spaces satisfying some curvature condition of pseudosymmetry type related to solutions of the P.J. Ryan problem of the equivalence of semisymmetry and Ricci-semisymmetry on hypersurfaces.

A class of four-dimensional warped products

Defever F., Deszcz R., Głogowska M., Goldberg V. V., Verstralen L.

Demonstratio Mathematica

2002

Vol. 35, nr 4

853-864

We investigate properties of 4-dimensional warped product manifolds satisfying a particular set of curvature conditions. As an application, we obtain a generalization of a pseudosymmetric property for Ricci-flat warped product spacetimes which was established previously in some special cases, including the Schwarzschild metric.

On some family of generalized Einstein metric conditions

Deszcz R., Hotloś M., Senturk Z.

Demonstratio Mathematica

2001

Vol. 34, nr 4

943-954

We prove that every Einstein manifold of dimension > 4 satisfies some pseudosymmetry type curvature condition. Basing on this fact we introduce a family of curvature conditions. We investigate non-Einstein manifolds satisfying one of these conditions. We prove that every such manifold is pseudosymmetric and satisfies other curvature conditions. We prove also an inverse theorem.

Curvature properties of some four-dimensional manifolds

Głogowska M.

Demonstratio Mathematica

2001

Vol. 34, nr 4

901-918

We present curvature properties of four-dimensional semi-Riemannian metrics related to semi-integrable almost Grassmann structures studied by M.A. Akivis and V.V. Goldberg in [2j.