Natural bundle

In differential geometry, a field in mathematics, a natural bundle is any fiber bundle associated to the higher order frame bundle ${\displaystyle F^{r}(M)}$, for some ${\displaystyle r\geq 1}$. In other words, its transition functions depend functionally on local changes of coordinates in the base manifold ${\displaystyle M}$ together with their partial derivatives up to order at most ${\displaystyle r}$.

The concept of a natural bundle was introduced in 1972 by Albert Nijenhuis as a modern reformulation of the classical concept of an arbitrary bundle of geometric objects.