V ーたまま、...。

The pattern is used in the following kind of situation:

you did a certain action and leave that situation (resulting from your action) as it is, and then you do the next action."

The expression of まま carries the meaning of 'as it is'.

Consider, for instance, the following examples, paying close attention to the meaning of V-ta mama.

Oftentimes, the V-ta mama form can be paraphrased by "V-nai de". Thus, the following are the equivalents of the above examples.