Natural operators transforming vector fields to the second order tangent bundle. (English) Zbl 0712.58003

Using a general method due to I. Kolář [Differential geometry and its applications, Proc. Conf., Brno/Czech. 1986, Math. Appl., East Eur. Ser. 27, 91-110 (1987; Zbl 0653.58003)] the author determines all natural operators \(T\to TT^ 2\) transforming every vector field on a manifold M into a vector field on its second order tangent bundle \(T^ 2M\), and deduces that all such operators form a 4-parameter family. There are also determined all natural transformations \(TT^ 2\to TT^ 2\) over the identity of the second order tangent functor.
Reviewer: N.Papaghiuc


58A05 Differentiable manifolds, foundations
58A20 Jets in global analysis


Zbl 0653.58003
Full Text: EuDML