All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
According to the Shaafi’i School of jurisprudence, the obligation in wiping over the head during ablution is to wipe part of the head. According to the Hanafi School of jurisprudence, it is sufficient to wipe over a quarter of the head, and according to the Hanbali and Maaliki Schools of jurisprudence, the entire head must be wiped over, which is better in order to be on the safe side.
Based on this view, it is obligatory on you to wipe over the entire head.
Allah knows best.