Abstract
Taking into account motivations from the geometrization of mathematical physics, we discuss the symmetrization of higher order jets and extension of connections. First we introduce an extension of a general connection Γ on a fibered manifold Y → M into an r -th order holonomic connection and we classify all second-order holonomic extensions of Γ. Then we study the general problem of symmetrization of jets. We introduce symmetrizations of higher-order semiholonomic and nonholonomic prolongations and we describe all symmetrizations of an r -th order semiholonomic prolongation j ¯ r .
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