Natural bundle explained

In mathematics, a natural bundle is any fiber bundle associated to the s-frame bundle

F ^{s(M)} for some s \geq 1 . It turns out that its transition functions depend functionally on local changes of coordinates in the base manifold M together with their partial derivatives up to order at most s .

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

TM of a manifold M