following 是在句中是现在分词的作用吗?是谓语成分吗?

问题描述:

following 是在句中是现在分词的作用吗?是谓语成分吗?
Finally,he writes his definitions,following the hard-and -fast rule that each definition must be based on what the sentences in front of him show about the meanings of the word.

是现在分词或介词=after...,不是谓语成分,是时间状语:在……之后.本句的主语的谓语是 writes.