$K$-contact structures on Lie groups

In this paper, left invariant $K$-contact structures on Lie groups are considered. The main results are Theorem 1 expressing the Ricci tensor of a Lie group $G$ by the Ricci tensor of a quotient space $M=G/F_0$, where $F_0$ is a one-parametrical subgroup of the Reeb field $\xi$, and Theorem 2 establishing the connection between the tensor $N^{(1)}$ of a contact metric structure on $G$ and the Nijenhuis tensor $N$ of the corresponding almost complex structure on $M=G/F_0$.