Özet
It is known that the Cartan hypersurfaces of dimension 6, 12 or 24 are non-quasi-Einstein, non-pseudosymmetric, Ricci-pseudosymmetric manifolds. In this paper we investigate quasi-Einstein hypersurfaces in semi-Riemannian space forms satisfying some Walker type identity. Among other things we prove that such hypersurfaces are Ricci-pseudosymmetric manifolds. Using certain result of Magid we construct an example of a quasi-Einstein non-pseudosymmetric Ricci-pseudosymmetric warped product which locally can be realized as a hypersurface in a semi-Riemannian space of constant curvature. In our opinion it is a first example of a hypersurface having the mentioned properties.
Orijinal dil | İngilizce |
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Makale numarası | 1250073 |
Dergi | International Journal of Mathematics |
Hacim | 23 |
Basın numarası | 7 |
DOI'lar | |
Yayın durumu | Yayınlandı - Tem 2012 |
Finansman
The first two named authors were supported by the grant 2 P03A 006 17 from the Polish State Committee of Scientific Research (KBN). The first named author was also supported by a grant of the Technische Universität Berlin (Germany).
Finansörler | Finansör numarası |
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KBN | |
Polish State Committee of Scientific Research | |
Technische Universität Berlin |