Displaying similar documents to “Higher order Grassmann fibrations and the calculus of variations.”

Some geometric aspects of the calculus of variations in several independent variables

David Saunders (2010)

Communications in Mathematics

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This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.

Homogeneous variational problems: a minicourse

David J. Saunders (2011)

Communications in Mathematics

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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 m . In this minicourse we discuss these problems from a geometric point of view.