Monotone point-to-set vector fields.

da Cruz Neto, J.X.; Ferreira, O.P.; Lucambio Pérez, L.R.

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We present an explicit formula for the Ruelle rotation of a nonsingular Killing vector field of a closed, oriented, Riemannian 3-manifold, with respect to Riemannian volume.

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

Irena Hinterleitner, Volodymyr A. Kiosak (2008)

Archivum Mathematicum

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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...