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$φ (Ric)$ -vector fields in Riemannian spaces

Irena Hinterleitner; Volodymyr A. Kiosak — 2008

Archivum Mathematicum

In this paper we study vector fields in Riemannian spaces, which satisfy $\nabla ϕ = μ$ , $𝐑𝐢𝐜$ , $μ = const.$ We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and $ϕ (Ric)$ -vector fields cannot exist simultaneously. It was found that Riemannian spaces with $ϕ (Ric)$ -vector fields of constant length have constant scalar curvature. The conditions for the existence of $ϕ (Ric)$ -vector fields in symmetric spaces are given....

On geodesic mappings preserving the Einstein tensor

Olena E. Chepurna; Volodymyr A. Kiosak; Josef Mikeš — 2010

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper there are discussed the geodesic mappings which preserved the Einstein tensor. We proved that the tensor of concircular curvature is invariant under Einstein tensor-preserving geodesic mappings.

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φ ( Ric ) -vector fields in Riemannian spaces

On geodesic mappings preserving the Einstein tensor

$φ (Ric)$ -vector fields in Riemannian spaces