Children know all about their parents, but parents are ignorant of their children. The only thing I can think of is to pass the name of the child class of interest as a parameter, then you could reference any static values of that class via $className::staticMemberName.
However, I have to be a bit suspicious of any design that requires such references. I mean, an abstract method could be extended by any number of other classes, so how would you know which child's static members you wanted to reference unless you did, in fact, specify that specific extending class?