Some differential-geometric aspects of the Lagrange variational problem

into extremals. Generalizing the same question dealt with earlier for Rie- mannian geometry [14], we ask for the points b e B such that the integral curve of X starting at b is itself a formal extremal. Modulo degeneracy problems, the answer in the case where L and S are time-independent is that they are the critical points of the function b ---. L(b, X(b)) restricted to the submanifold b e B X(b) S} of B.