منابع مشابه
Horizontal Subbundle on Lie Algebroids
Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to construction of a better framework on Lie algebriods. In this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a Lie algebroid and then we show that any linear connection on a Lie algebroid generates a horizontal subbundle and vice versa. The same correspo...
متن کاملPoisson Structures on Lie Algebroids
In this paper the properties of Lie algebroids with Poisson structures are investigated. We generalize some results of Fernandes [1] regarding linear contravariant connections on Poisson manifolds at the level of Lie algebroids. In the last part, the notions of complete and horizontal lifts on the prolongation of Lie algebroid are studied and their compatibility conditions are pointed out.
متن کاملVariational Calculus on Lie Algebroids
It is shown that the Lagrange’s equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.
متن کاملLie Algebroids and Lie Pseudoalgebras
Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2-5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a gen...
متن کاملOmni-lie Algebroids *
A generalized Courant algebroid structure is defined on the direct sum bundle DE ⊕ JE, where DE and JE are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a structure is called an omni-Lie algebroid since it is reduced to the omni-Lie algebra introduced by A.Weinstein if the base manifold is a point. We prove that any Lie algebroid structure on E is characteri...
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ژورنال
عنوان ژورنال: Annals of Global Analysis and Geometry
سال: 2013
ISSN: 0232-704X,1572-9060
DOI: 10.1007/s10455-013-9368-y