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2013 Generalized Lie Algebroids and Connections over Pair of Diffeomorphic Base Manifolds
Constantin M. Arcus¸
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J. Gen. Lie Theory Appl. 7: 1-32 (2013). DOI: 10.4303/jglta/G111202


Extending the definition of Lie algebroid from one base manifold to a pair of diffeomorphic base manifolds, we obtain the generalized Lie algebroid. When the diffeomorphisms used are identities, then we obtain the definition of Lie algebroid. We extend the concept of tangent bundle, and the Lie algebroid generalized tangent bundle is obtained. In the particular case of Lie algebroids, a similar Lie algebroid with the prolongation Lie algebroid is obtained. A new point of view over (linear) connections theory of Ehresmann type on a fiber bundle is presented. These connections are characterized by a horizontal distribution of the Lie algebroid generalized tangent bundle. Some basic properties of these generalized connections are investigated. Special attention to the class of linear connections is paid. The recently studied Lie algebroids connections can be recovered as special cases within this more general framework. In particular, all results are similar with the classical results. Formulas of Ricci and Bianchi type and linear . connections of Levi-Civita type are presented.


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Constantin M. Arcus¸. "Generalized Lie Algebroids and Connections over Pair of Diffeomorphic Base Manifolds." J. Gen. Lie Theory Appl. 7 1 - 32, 2013.


Published: 2013
First available in Project Euclid: 23 July 2015

zbMATH: 1268.58006
MathSciNet: MR3047637
Digital Object Identifier: 10.4303/jglta/G111202

Primary: 00A69 , 53B05 , 58B34

Rights: Copyright © 2013 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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