§1. In the suffragan dioceses, a metropolitan is competent: 1/ to exercise vigilance so that the faith and ecclesiastical discipline are observed carefully and to inform the Roman Pontiff of abuses, if there are any; 2/ to conduct a canonical visitation for a cause previously approved by the Apostolic See if a suffragan has neglected it; 3/ to designate a diocesan administrator according to the norm of cann. 421, §2, and 425, §3.
§2. Where circumstances demand it, the Apostolic See can endow a metropolitan with special functions and power to be determined in particular law.
§3. The metropolitan has no other power of governance in the suffragan dioceses. He can perform sacred functions, however, as if he were a bishop in his own diocese in all churches, but he is first to inform the diocesan bishop if the church is the cathedral.
Source: Code of Canon Law (Vatican.va)