In differential geometry, a field in mathematics, a natural bundle is any fiber bundle associated to the higher order frame bundle F r ( M ) {\displaystyle F^{r}(M)} , for some r ≥ 1 {\displaystyle r\geq 1} . In other words, its transition functions depend functionally on local changes of coordinates in the base manifold M {\displaystyle M} together with their partial derivatives up to order at most r {\displaystyle r} .
In differential geometry, a field in mathematics, a natural bundle is any fiber bundle associated to the higher order frame bundle F r ( M ) {\displaystyle F^{r}(M)} , for some r ≥ 1 {\displaystyle r\geq 1} . In other words, its transition functions depend functionally on local changes of coordinates in the base manifold M {\displaystyle M} together with their partial derivatives up to order at most r {\displaystyle r} .
Source: Wikipedia "Natural bundle" · CC BY-SA 4.0
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