Why were centralized empires so much less prominent in india than in china?

There were numerous reasons. For starters, India was invaded more than China and this led to a higher independence of local regions over the idea of a great state. Secondly, India was culturally much more diverse than China and didn't have a strong unifying identity. In addition, India had the caste system that was very local when it came to support of localized governments which did not exist in China.