CR structures, k-contact structures, and generalized Sasakian structures

In previous work (arXiv:2205.12067), we defined a notion of a generalized Sasakian structure in the context of generalized contact geometry, the odd dimensional analogue of generalized complex geometry introduced by Hitchin and Gualtieri. We show here that k-contact manifolds are generalized Sasakian if and only if they are classically Sasakian. We show also that strictly pseudo-convex CR manifolds are always generalized Sasakian.