On some integration methods for connections on fibered manifolds

Olga Krupkov\'a and Alexandr Vondra

Abstract. In the paper relations between (Ehresmann) connections
on jet prolongations of fibered manifolds are studied. Two indirect
integration methods for these connections are proposed, generalizing
both the ``method of characteristics" from the theory of exterior
differential systems and the ``method of fields of extremals"
(Hamilton-Jacobi integration method) from the classical calculus
of variations to (non-variational) first and second-order partial or ordinary
differential equations, explicitly solved with respect to the highest
derivatives.

Keywords. (Ehresmann) connection,
horizontal distribution, integral sections, integration of connections.

MS classification. 35A30, 53C05, 70H20.