  In this paper we study the second fundamental form of the Prym map $P_{g,r}:
R_{g,r} \rightarrow {\mathcal A}^{\delta}_{g-1+r}$ in the ramified case $r>0$.
We give an expression of it in terms of the second fundamental form of the
Torelli map of the covering curves. We use this expression to give an upper
bound for the dimension of a germ of a totally geodesic submanifold, and hence
of a Shimura subvariety of ${\mathcal A}^{\delta}_{g-1+r}$, contained in the
Prym locus.
