Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertical and complete lifts of sections of a (dual) vector bundle and
  Legendre duality   Supplementary comments about generalized Lie algebroids are presented and a
new point of view over the construction of the Lie algebroid generalized
tangent bundle of a (dual) vector bundle is introduced. Using the general
theory of exterior differential calculus for generalized Lie algebroids, a
covariant derivative for exterior forms of a (dual) vector bundle is
introduced. Using this covariant derivative, the complete lift of an arbitrary
section of a (dual) vector bundle is discovered. A theory of Legendre type and
Legendre duality between vertical and complete lifts is presented. Finally, a
duality between Lie algebroids structures is developed.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th