John, knowing that his wife was expecting a baby, started to take a course on baby care. = John, who knew that his wife was expecting a baby, started to take a course on baby care.
As I know,'knowing that his wife was expecting a baby'is supplementive phrase for John. In Comprehensive Grammar of the English Language, 'knowing that his wife was expecting a baby' also means'who knew that his wife was expecting'.
With this theory, I wonder if I'm right about sen tenses below.
Julia, being a nun, spent much of her life in prayer and meditation. = Julia, who was a nun, spent much of her life in prayer and meditation.
Julia, wearing a hat, looks beautiful. = Julia who wears a heat, looks beautiful.