As a permanent resident you are taxed on your worldwide income. How much of that income is taxable depends upon your personal situation. Consult with a CPA or Tax Attorney who handles international tax matters.
If you have no income on a worldwide basis you do not have a U.S. filing requirement.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.