We consider the centralizer of Reeb vector field of a contact Lie group with a left invariant Riemannian metric while contact structure is left invariant. Then we decompose the Lie algebra of this Lie groups to centralizer of Reeb vector field and its orthogonal complement and using this decomposition the contact Lie group is investigated. Furthermore, in last section a special automorphism is defined and studied which it keeps the contact form.
"Centralizer of Reeb Vector Field in Contact Lie Groups." J. Geom. Symmetry Phys. 48 23 - 31, 2018. https://doi.org/10.7546/jgsp-48-2018-23-31