A U.S. permanent resident is treated the same as a U.S. citizen for federal income tax purposes. As far as income tax is concerned, it won't make any difference whether you are a citizen or a permanent resident. You will be required to file U.S. tax returns as long as you maintain your permanent resident status, even if you are no longer living in the U.S. In order to stop filing U.S. tax returns you would have to take steps to abandon your resident status. Doing that, of course, might affect your ability to return to the U.S. if you wanted to.
The rules for situations such as yours are very complex. You should consult a lawyer who is familiar with all of the applicable immigration and tax rules. Don't rely on anonymous advice from the internet, not even mine.
