On curvature properties of certain quasi-Einstein hypersurfaces

Ryszard Deszcz*, Marian Hotlo, Zerrin EntÜrk

*Bu çalışma için yazışmadan sorumlu yazar

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19 Atıf (Scopus)

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 dilİngilizce
Makale numarası1250073
DergiInternational Journal of Mathematics
Hacim23
Basın numarası7
DOI'lar
Yayın durumuYayınlandı - 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).

FinansörlerFinansör numarası
KBN
Polish State Committee of Scientific Research
Technische Universität Berlin

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