The vp has no special domain except:...
1) Cast a tie-breaking vote in the senate, and
2) Step in as president if the prez cannot serve.
Anything else the veep might do is by special arrangement that any given president may or may not make. Gore liked science and space, so Clinton gave him some special projects in that area. Cheney liked going after Saddam, so Bush gave Cheney some responsibilities in that area.