I want to ask you if you know any reference where the second fundamental theorem for $SO(n)$ is stated and proved. I have been looking for it but my quest has been useless. By classical invariant theory, we know that the ring of invariants for $SO(m,n)$ is generated by the scalar products and the determinants, but I want to know what are the relations between them. Is this an open problem? I couldn't find any hints on the internet.
Thank you.