The geodesic flow on nilpotent Lie groups of steps two and three
The geodesic flow on nilpotent Lie groups of steps two and three
<p style='text-indent:20px;'>The goal of this paper is the study of the integrability of the geodesic flow on <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math></inline-formula>-step nilpotent Lie groups, k = 2, 3, when equipped with a left-invariant metric. Liouville integrability is proved in low dimensions. Moreover, it is shown that complete families of first …