Left-invariant hypercontact structures on three-dimensional Lie groups
The authors prove that a 3-manifold \(M\) is parallelizable if and only if one of the following assertions holds: {\parindent=0.6cm\begin{itemize}\item[(i)] \(M\) admits an almost contact metric 3-structure; \item[(ii)] \(M\) admits a mixed metric 3-structure. \end{itemize}} As a consequence, they show that a three-dimensional Lie groups \(G\) admits a left-invariant hypercontact metric structure if and only if the universal covering \(\tilde{G}\) is \(\mathrm{SU}(2)\) or \(\tilde{\mathrm{SL}}(2,{\mathbf R})\).
scientific article; zbMATH DE number 6384179
scientific article