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.

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.