Invariant differential forms?

Question

In the first page of the paper "On the spaces of maps inducing isomorphic connections" by T.R. Ramadas, one can read that the automorphisms of a connection $\nabla$ on a principal $G$-bundle $\pi:P \longrightarrow M$, denoted by $\mathsf{Aut}(\nabla)$, are those $G$-equivariant maps $P \longrightarrow P$ which cover the identity of $M$ and leave the connection $\nabla$ invariant.
Now, my question is: what does "leave invariant" mean here? Take a map $f$ in $\mathsf{Aut}(\nabla)$. Does this mean that the pull-back $f^*\nabla = \nabla$?