"1"^^ . "0"^^ . . "CZ - \u010Cesk\u00E1 republika" . "Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold"@en . "1"^^ . "14310" . "[D97A4A16E94A]" . "0044-8753" . "18"^^ . . "Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold" . . . . "Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$. We classify all natural 0-order vector fields and 2-vector fields on $TM$ generated by $g$ and $K$. We get that all natural vector fields are linear combinations of the vertical lift of $u\\in T_xM$ and the horizontal lift of $u$ with respect to $K$. Similarlz all natural 2-vector fields are linear combinatins of two canonical 2-vector fields induced by $g$ and $K$. Conditions for natural vector fields and natural 2-vector fields to define a Jacobi or a Poisson structure on $TM$ are disscused."@en . "P(GA201/99/0296), Z(MSM 143100009)" . . . "Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$. We classify all natural 0-order vector fields and 2-vector fields on $TM$ generated by $g$ and $K$. We get that all natural vector fields are linear combinations of the vertical lift of $u\\in T_xM$ and the horizontal lift of $u$ with respect to $K$. Similarlz all natural 2-vector fields are linear combinatins of two canonical 2-vector fields induced by $g$ and $K$. Conditions for natural vector fields and natural 2-vector fields to define a Jacobi or a Poisson structure on $TM$ are disscused." . "Archivum Mathematicum" . . "RIV/00216224:14310/01:00004221!RIV/2002/MSM/143102/N" . . "Poisson structure, pseudo-Riemannian manifold, natural operator"@en . . "Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold"@en . . . . . "37" . "Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold" . "Jany\u0161ka, Josef" . . "688278" . . . "143" . "2" . "RIV/00216224:14310/01:00004221" . "0"^^ .