Context: I'm reading about tetrad formalism in General Relativity. Thus, a tetrad is something as $e_I=e^\mu_I\partial_\mu$ where the greek indices are related to a chart and the Latin indice is related to internal space $\mathbb{R}^4$ (Minkowski space). Then you can define an internal metric $n_{IJ}& and so on...
Question: What would be (or where I can find) a formal definition of what an internal space is?