The geodesic flow on nilmanifolds associated to graphs
Gabriela P. Ovando
TL;DR
This paper investigates the geodesic flow on nilmanifolds linked to graphs, focusing on constructing first integrals to demonstrate integrability and providing examples of both integrable and non-integrable flows.
Contribution
It introduces methods for constructing first integrals on nilmanifolds associated to graphs and presents new examples of integrable and non-integrable geodesic flows.
Findings
Complete integrability achieved on some compact quotients
Explicit examples of integrable geodesic flows
Examples of non-integrable geodesic flows
Abstract
In this work 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. Also examples of integrable geodesic flows and of non-integrable ones are shown.
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