I've been reading a little bit about the definition of symmetries on General Relativity, and they are related with the concept of *Killing vector*, i.e., vectors along which the Lie derivative of the metric vanishes $\mathcal{L}_X g =0$.

However, afaik the most symmetric geometrical object is the Ricci tensor (see the post), and the a vector $X$ satisfying $\mathcal{L}_X \text{Ric} = 0$ is known as a *collineation* of the Ricci tensor.

I'd like to know whether is possible to define a sort of Lie derivative for a (general) connection, or a way to somehow define the symmetries of a connection.