adverbial participle

Wiktionary

1. n. linguistics A participle that modifies a verb in same sentence and which is equivalent to an adverbial clause in English. Adverbial participles may denote time, condition, cause, concession, manner, means, purpose, or attendant circumstance. Adverbial participles are found in such languages as Greek, Lithuanian, Hindi, Hungarian, Tamil, Polish, and Russian. In Russian, the adverbial participle usually translates to while + gerund (while doing) or having + past participle (having done).