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Natural bundle

From Wikipedia, the free encyclopedia

In mathematics, a natural bundle is any fiber bundle associated to the s-frame bundle for some . It turns out that its transition functions depend functionally on local changes of coordinates in the base manifold together with their partial derivatives up to order at most .[1]

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.[2]

An example of natural bundle (of first order) is the tangent bundle of a manifold .

Notes

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  1. ^ Palais, Richard; Terng, Chuu-Lian (1977), "Natural bundles have finite order", Topology, 16: 271–277, doi:10.1016/0040-9383(77)90008-8, hdl:10338.dmlcz/102222
  2. ^ A. Nijenhuis (1972), Natural bundles and their general properties, Tokyo: Diff. Geom. in Honour of K. Yano, pp. 317–334

References

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