Abstract
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.
| Original language | English |
|---|---|
| Article number | 1250073 |
| Journal | International Journal of Mathematics |
| Volume | 23 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - Jul 2012 |
Funding
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).
| Funders | Funder number |
|---|---|
| KBN | |
| Polish State Committee of Scientific Research | |
| Technische Universität Berlin |
Keywords
- pseudosymmetric hypersurface
- pseudosymmetry type manifold
- quasi-Einstein hypersurface
- QuasiEinstein manifold
- Ricci-pseudosymmetric hypersurface
- Walker type identity
- warped product