On Double Vector Bundles

Details On Double Vector Bundles On Double Vector Bundles

2011-03-04

arxiv.org/abs/1103.0866v1

Mathematics

Differential Geometry

19 Pages

Scientific paper

In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.

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