On certain natural transformations between connections

Miroslav Doupovec and Alexandr Vondra

Abstract. We determine all natural transformations of $J^1(J^1(Y\to X)\to Y)$
into $J^1(J^1(Y\to X)\to X)$ over the identity of $J^1(Y\to X)$. Then we
interpret the analytical result geometrically and correlate it with
the geometry of connections on $Y\to X$.

Keywords. Natural operator, jet prolongation, connection.

MS classification. 53C05, 58A20.