On 2-Killing vector fields in almost contact metric geometry

We characterize a 2-Killing Reeb vector field of a contact metric manifold, we describe the 2-Killing vector fields pointwise collinear with the Reeb vector field of the structure, and we study them in the general Riemannian case. On the other hand, we obtain some properties when the Reeb vector field is 2-Killing and the manifold is a Ricci soliton, a Yamabe soliton, a hyperbolic Ricci soliton, or a hyperbolic Yamabe soliton with potential vector field pointwise collinear with the Reeb vector field of the structure.