Displaying similar documents to “Lie algebroids and mechanics”

On higher order geometry on anchored vector bundles

Paul Popescu (2004)

Open Mathematics

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Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.

Calculus on Lie algebroids, Lie groupoids and Poisson manifolds

Charles-Michel Marle

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We begin with a short presentation of the basic concepts related to Lie groupoids and Lie algebroids, but the main part of this paper deals with Lie algebroids. A Lie algebroid over a manifold is a vector bundle over that manifold whose properties are very similar to those of a tangent bundle. Its dual bundle has properties very similar to those of a cotangent bundle: in the graded algebra of sections of its exterior powers, one can define an operator d E similar to the exterior derivative....

Lectures on generalized complex geometry and supersymmetry

Maxim Zabzine (2006)

Archivum Mathematicum

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These are the lecture notes from the 26th Winter School “Geometry and Physics", Czech Republic, Srní, January 14 – 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely to two-dimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kähler and...

On the second order absolute differentiation

Cabras, Antonella, Kolář, Ivan

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In this paper the authors compare two different approaches to the second order absolute differentiation of a fibered manifold (one of them was studied by the authors [Arch. Math., Brno 33, 23-35 (1997; Zbl 0910.53014)]. The main goal is the extension of one approach to connections on functional bundles of all smooth maps between the fibers of two fibered manifolds over the same base (we refer to the book “Natural Operations in Differential Geometry” [Springer, Berlin (1993; Zbl 0782.53013)]...