ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS

. We nd all FM m -natural operators Atransforming torsionfree classical linear connections ∇on m-manifolds M into base preservingbred maps A(∇) : J r Y → J r Y for FM m -objects Y with bases M,where J r , J r are the semiholonomic and holonomic jet functors of orderr on the category FM m of bred manifolds with m-dimensional basesand their bred maps with embeddings as base maps. 0. IntroductionAll manifolds considered in the paper are assumed to be nite dimensional,without boundaries, Hausdor, second countable and smooth (of class C ∞ ).Maps between manifolds are assumed to be of class C ∞ .The classical theory of higher order jets was introduced by C. Ehresmann,[2]. For semiholonomic jets, we refer to the paper by P. Libermann, [8]. Higherorder jets are a very powerful tool in dierential geometry and in mathematicalphysics. For example, holonomic jets globalize the theory of dierential systemsand semiholonomic jets play an important role in the calculus of variations andin the theory of partial dierential equations, [11], [12]. The theory of jets andconnections forms the geometrical background for eld theories and theoreticalphysics, [7], [9]. Holonomic and semiholonomic prolongation functors J