What was the christian church that developed in the byzantine empire called?

Explanation:

Roman Emperor Constantine relocated his capital city to Byzantium in the 4th century (renaming it Constantinople).  That accelerated the process of division between the western church, which became the Roman Catholic Church, and the eastern church, which became the Eastern (Greek) Orthodox Church.

Tensions between the western, Latin-speaking half of the church and the eastern, Greek-speaking half of the church built up over centuries of time.  They argued over some doctrinal matters, such as whether the Holy Spirit proceeds from the Father and the Son (the West's confession) or from the Father alone (which was the East's insistence).  But ultimately there would be a struggle between the two halves of the church about authority in the church.  As the office of the Bishop of Rome sought to claim more universal authority for itself as the Papacy, the Patriarchs (church fathers) who governed in Constantinople objected.  By the 11th century, the two churches split from each other and went their separate ways.

honestly it just comes down to the