Final answer:
The division of Kiev's realm among Yaroslav's sons weakened the central authority, leading to fragmentation, internal strife, and vulnerability to external threats, contributing to Kiev's decline.
Step-by-step explanation:
Yaroslav's decision to divide his realm among his sons helped cause Kiev's decline by fragmenting the state into rival principalities. This division weakened the central authority and made it more difficult for the region to unite against external threats or to maintain internal order. Such fragmentation of power is a classic element in the fall of an empire, often leading to a weakening of military strength, economic instability, and internal conflict, all of which make the state more vulnerable to external pressures and eventual collapse. This is analogous to the division of the Roman Empire after the death of Theodosius I, and the Byzantine Empire's struggles with the aristocracy and powerful dynatoi, as seen in history.