Monday, June 17, 2013

1306.3379 (Michał Jóźwikowskiy et al.)

Higher algebroids with applications to variational calculus    [PDF]

Michał Jóźwikowskiy, Mikołaj Rotkiewicz
Motivated by reduction of higher tangent bundles we introduce the concept of a higher algebroid -- an object generalizing the notion of an almost Lie algebroid. As a main application we develop a geometric framework for higher-order variational calculus on algebroids (together with the associated Euler-Lagrange equations and momenta). Within a single formalism we cover variational problems on higher tangent bundles, first-order problems on Lie algebroids and higher-order problems reduced by symmetries. We study natural examples of higher algebroids and the associated variational problems.
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