Geodesic flow refers to the motion along geodesics, which are the shortest paths between points on a manifold. In the context of differential geometry and topology, geodesics can be understood as the natural generalization of straight lines in curved spaces, and geodesic flow describes how points move along these paths under the influence of a dynamical system. This concept is crucial for understanding the geometry of Lie groups and their applications in various fields, including physics and engineering.
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