A world where Rajiv Gandhi survives the assassination of 1991 would likely see a continuation of his economic liberalization policies, potentially leading to faster economic growth in India but also potentially exacerbating existing social and economic inequalities. His continued leadership might have altered India's foreign policy trajectory, impacting its relationships with the Soviet Union (given its collapse shortly after the assassination) and the West. The absence of his assassination could also have significantly altered the political landscape of India, influencing the rise and fall of various political parties and figures.

The non-occurrence of the Velvet Revolution in Czechoslovakia would have profound implications for Central and Eastern Europe. The Soviet Union, without the pressure of a successful revolution in Czechoslovakia, might have maintained a firmer grip on its satellite states, delaying or preventing the collapse of the Eastern Bloc. This could have led to a prolonged period of communist rule in these countries, with significant consequences for their economic development, political freedoms, and social structures. The absence of the Velvet Revolution would also have ripple effects on the broader geopolitical landscape, potentially altering the trajectory of the Cold War and the reunification of Germany.

The failure of the Eastern Roman Empire's restoration in 1261 would have dramatically altered the course of Byzantine history. Without the recapture of Constantinople, the empire might have continued its decline, potentially falling to the Ottoman Turks earlier than it did historically. This could have resulted in a significantly different geopolitical map of the Eastern Mediterranean, with far-reaching consequences for trade routes, cultural exchange, and the balance of power in the region. The absence of a restored Byzantine Empire would also have impacted the development of various successor states and the spread of various religious and cultural influences.

Combining these three alternate scenarios creates a complex and fascinating hypothetical world. India under a long-reigning Rajiv Gandhi, a continued Soviet-dominated Eastern Europe, and a weakened or non-existent Byzantine Empire would interact in unpredictable ways. For example, India's economic growth might have been affected by the continued instability in Eastern Europe, impacting trade and global markets. The absence of the Velvet Revolution could have influenced the Soviet Union's response to India's growing economic power. The lack of a restored Byzantine Empire could have altered the flow of trade and cultural exchange between East and West, potentially impacting India's interactions with the West. The overall picture is one of significant divergence from our historical timeline, with numerous potential branching points and unforeseen consequences. The interplay between these three major alternate historical events would create a unique and richly detailed alternate history, ripe for exploration and storytelling.