I am trying to understand the Chern-Moser tensor in CR geometry. What I learn is that it is very similar to Weyl tensor in Riemannian geometry. So I find in wiki about Weyl tensor: http://en.wikipedia.org/wiki/Weyl_tensor
Weyl tensor satisfies some identities, for example, it's trace-free, and it satisfies the Bianchi identity.
My question is that: Does Chern-Moser tensor have the similar properties? More precisely, is it trace-free? Does it satisfies some kind of Bianchi identity? Is there any other interesting propertites about Chern-Moser tensor? Also I find that there are not many references about Chern-Moser tensor. Are there any good references? Thanks.