Abstract
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and derive some obstruction results to the existence of left invariant contact structures on Lie groups.
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Diatta, A. Riemannian geometry on contact Lie groups. Geom Dedicata 133, 83–94 (2008). https://doi.org/10.1007/s10711-008-9236-2
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DOI: https://doi.org/10.1007/s10711-008-9236-2