**Beiträge zur Algebra und Geometrie
**

Contributions to Algebra and Geometry

Vol. 39, No. 2, pp. 283-290 (1998)

#
On Holonomicity Criteria in Second Order Geometry

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I. Kolar

Department of Algebra and Geometry, Faculty of Science, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic

**Abstract:** We introduce the intrinsic exterior differential of the contact morphism on the first jet prolongation of a fibered manifold $Y$. Using this concept, we deduce a holonomicity criterion for the second semi-holonomic prolongation of $Y$ and we clarify that this is closely related to several classical procedures. The same idea is applied to the bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base.

**Keywords:** contact morphism, intrinsic exterior differential, semi-holonomic 2-jet, connection, $G$-structure, bundle of smooth fiber maps

**Classification (MSC91):** 58A20, 53C05, 53C10

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