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A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension . In this minicourse we discuss these problems from a geometric point of view.
We review the approach to the calculus of variations using Ehresmann's theory of jets. We describe different types of jet manifold, different types of variational problem and different cohomological structures associated with such problems.
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