Natural Lagrangian structures. (English) Zbl 0572.58007

Differential geometry, 14th Semest. S. Banach Int. Math. Cent., Warsaw 1979, Banach Cent. Publ. 12, 185-210 (1984).
[For the entire collection see Zbl 0546.00020.]
The author discusses the fundamental properties of a specific class of integral variational problems in fiber bundles, which are usually called generally invariant. The material is divided up as follows: in the first section the differential invariants are defined and some of their properties are sketched. The odd base forms and the projectable vector fields on a fiber manifold are the object of the second section. In the last section the Lagrangian structures are introduced and some of their properties are pointed out. Written in very clear style, this survey paper will be very useful for all those who work on these topics.
Reviewer: M.Puta


37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58C99 Calculus on manifolds; nonlinear operators
58E30 Variational principles in infinite-dimensional spaces


Zbl 0546.00020