Muslim architects copied Byzantine architecture and in particular the dome. The first great work of monumental Islamic architecture, the Dome of the Rock in Jerusalem was clearly the result of Byzantine influence. read more
I would not agree that Muslim and Byzantine art look similar however. While there are certainly stylistic cross influences, the focus of Byzantine art was the icon, which was a representational image usually of Jesus or Mary. Such images were and are generally prohibited in Islamic art because they are regarded as idolatry. read more
Basically, they look very different to me, as far as figurative art forms are concerned. Byzantine art is centered upon religion, there are Saints everywhere, on icons and on church walls. Islamic art is highly decorative but you will find no representation of persons at all (with few exceptions, mainly in Persia). read more
Like many cultures before it, the Byzantine Empire continued its reign, so to speak, as a major influencer in the areas of art and architecture long after its fall. Islamic territories, for instance, adopted a wide range of styles and incorporated elaborate mosaics on the walls of each structure, created from the hands of Christian artists. read more