Abstract
We show that every five-dimensional Sasakian Lie algebra with trivial center is $\varphi$-symmetric. Moreover starting from a particular Sasakian structure on the Lie group $SL(2,\mathbb{R})\times\text{Aff}(\mathbb{R})$ we obtain a family of contact metric $(k,\mu)$ structures whose Boeckx invariants assume all values less than $-1$.
Citation
E. Loiudice. A. Lotta. "On five dimensional Sasakian Lie algebras with trivial center." Osaka J. Math. 55 (1) 39 - 49, January 2018.