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

Doupovec, Miroslav

Čas. Pěstování Mat. 115, No. 1, 64-72 (1990).

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

MSC:

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

Keywords:

natural operators; second order tangent bundle; natural transformations; second order tangent functor

Citations:

Zbl 0653.58003