GEOMETRIC-THEORY OF TIME-DEPENDENT SINGULAR LAGRANGIANS

The geometry of jet bundles is used for obtaining a geometric approach to time-dependent Lagrangian systems, both in the regular and singular case. Generalized symmetries are introduced as being given by vector fields along the projection pi1,0. This approach is shown to be very useful for giving a one-to-one correspondence between symmetries and constants of motion and allows a geometric version of the Second Noether Theorem. The theory is illustrated by several examples in which the gauge symmetries are explicitly found.