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4-dimensional anti-Kähler manifolds and Weyl curvature

Jaeman Kim (2006)

Czechoslovak Mathematical Journal

On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.

η -Ricci Solitons on η -Einstein ( L C S ) n -Manifolds

Shyamal Kumar Hui, Debabrata Chakraborty (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The object of the present paper is to study η -Ricci solitons on η -Einstein ( L C S ) n -manifolds. It is shown that if ξ is a recurrent torse forming η -Ricci soliton on an η -Einstein ( L C S ) n -manifold then ξ is (i) concurrent and (ii) Killing vector field.

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 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....

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