My partners car is venting oil mist from a pipe that is underneath the inlet manifold pipes. The pipe in question is made of rubber, a bit like a vacuum pipe, but I have no Idea what it is or what it does!

At first I though it was a crank breather pipe, but not so sure anymore

I have a couple of photos to show you all what I am referring to highlighting where the pipe is and the crack in it

First image is of the whole inlet from the front showing where the pipe is, second image is a close up between the inlet pipe gaps showing the pipe and crack, and third image is of the opposite end of the pipe from the crack showing the T section it attaches to

Can someone please ID the pipe in question, and where the best place would be to purchase a replacement?

Thanks in advance!