Marian Hotloś

Curvature properties of Gödel metric

The main aim of this paper is to investigate the geometric structures admitting by the Godel spacetime which produces a new class of semi-Riemannian manifolds. We also consider some extension of Godel metric.

ON CURVATURE PROPERTIES OF CERTAIN QUASI-EINSTEIN HYPERSURFACES

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.

A note on almost kähler manifolds

For anyn ≥ 2, we give examples of almost Kähler conformally flat manifoldsM2n which are not Kähler. We discuss the meaning of these examples in the context of the Goldberg conjecture on almost Kahler manifolds.