  We study differential forms on the universal vector extension $A^\natural$ of
an abelian scheme $A$ in characteristic zero, and derive a new construction of
the $D$-group scheme structure on $A^\natural$. This gives, in particular, a
rather simple description of the Gauss--Manin connection on the de Rham
cohomology of $A$ in terms of global algebraic differential forms on
$A^\natural$. The key ingredient is the computation of the coherent cohomology
of $A^{\natural}$, due to Coleman and Laumon.
