Geodesic
$K$-contact structures on Lie groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2011), pp. 47-54

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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 $M=G/F_0$.
Keywords: contact Lie groups, contact metric structures, Sasakian structure, $K$-contact structures. 
@article{VTGU_2011_1_a5,
     author = {Y. V. Slavolyubova},
     title = {$K$-contact structures on {Lie} groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {47--54},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2011_1_a5/}
}
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Y. V. Slavolyubova. $K$-contact structures on Lie groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2011), pp. 47-54. http://geodesic.mathdoc.fr/item/VTGU_2011_1_a5/