Janyška, Josef Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold. (English) Zbl 1090.58007 Arch. Math., Brno 37, No. 2, 143-160 (2001). Let \(M\) be a manifold with a pseudo-Riemannian metric \(g\) and a linear symmetric connection \(K\). The author classifies all natural \(0\)-order vector fields \(E\) and \(2\)-vector fields \(\Lambda \) on \(TM\) generated by \(g\) and \(K\). Conditions for \((E,\Lambda )\) to define a Jacobi or Poisson structure on \(TM\) are discussed. Reviewer: Ivan Kolář (Brno) Cited in 3 Documents MSC: 58A32 Natural bundles 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 58A20 Jets in global analysis 53D17 Poisson manifolds; Poisson groupoids and algebroids Keywords:Poisson structure; pseudo-Riemannian manifold; natural operator PDFBibTeX XMLCite \textit{J. Janyška}, Arch. Math., Brno 37, No. 2, 143--160 (2001; Zbl 1090.58007) Full Text: EuDML EMIS