Proceedings of the 2nd Summer Conference Numerical Modelling in Continuum Mechanics. Preface
[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.
A product preserving functor is a covariant functor from the category of all manifolds and smooth mappings into the category of fibered manifolds satisfying a list of axioms the main of which is product preserving: . It is known that any product preserving functor is equivalent to a Weil functor . Here is the set of equivalence classes of smooth maps and are equivalent if and only if for every smooth function the formal Taylor series at 0 of and are equal in . In this paper all...