Symmetries of vector exterior differential systems and the inverse problem in second-order Ostrograds’kii mechanics. (English) Zbl 0957.58003

The author recalls the vector bundle valued differential forms and exterior systems. Then he introduces a new kind of equivalence in order to reformulate the usual concepts of symmetries and infinitesimal symmetries of systems of differential equations: two exterior differential systems are called equivalent if the sets of their solutions coincide, the symmetry is a transformation which changes a given system into an equivalent system.
It is not easy to effectively apply this new conception, a simple example from the relativistic mechanics is nevertheless briefly mentioned.


58A15 Exterior differential systems (Cartan theory)
58E30 Variational principles in infinite-dimensional spaces
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