How do sociopaths use body language to manipulate people?
Firstly, sociopathy is a very difficult diagnosis to make (and technically this formal diagnosis does not exist anymore - it is an old term for what is now referred to as antisocial personality disorder).
Sociopaths are seemingly well adjusted individuals who socially seem to feel and experience like everyone else. Under this mask is a very skilled manipulator who lives for his own power and selfish gain at the cost of others without any remorse.
Sociopaths can mimic the full range of human behaviour and emotions in their body language depending on what exactly their aim is in a given situation. A sociopath's body language can range from direct eye contact to the point of an uncomfortable stare to avoidance of eye contact - depending on whether they want to intimidate; or mimic embarrassment or shame.
Thus, to answer your question - sociopaths utilises the full spectrum of human behaviour and emotions through mimicking to manipulate people.