The geodesic flow on nilmanifolds associated to graphs

We study the geodesic flow on nilmanifolds associated to graphs. We are interested in the construction of first integrals to show complete integrability on some compact quotients. We start on the corresponding Lie group equipped with a left-invariant metric, which is induced to the quotients. Also examples of integrable geodesic flows and of non-integrable ones are shown.Fil: Ovando, Gabriela Paola. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Departamento de Matemática y Estadística; Argentin