Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold
| Authors | |
|---|---|
| Year of publication | 2001 |
| Type | Article in Periodical |
| Magazine / Source | Archivum Mathematicum |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.emis.de/journals |
| Field | General mathematics |
| Keywords | Poisson structure; pseudo-Riemannian manifold; natural operator |
| Description | 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. |
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