Integrable geodesic flows on Riemannian manifolds: Construction and Obstructions

TL;DR

This paper reviews recent and classical results on integrable geodesic flows on Riemannian manifolds, focusing on construction methods and topological obstructions, and discusses open problems in the field.

Contribution

It provides a comprehensive overview of known results and highlights open problems regarding integrability and topological obstructions in geodesic flows.

Findings

Summary of classical and recent results on integrable geodesic flows

Identification of topological obstructions to integrability

Discussion of open problems in the field

Abstract

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.