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Geodesic flow on Riemannian manifolds 1
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The general idea behind the concept of geodesics is the generalisation of straight lines in
Euclidian space to Riemannian manifolds. A geodesic will be a constantly paramatrized,
smooth curve on the manifold, that is locally the shortest curve connecting two points with each other. They are of great importance in the further study of Riemannian Geometry, as well as in theoretical physics, in particular in
General Relativity, where they are the trajectories of test objects moving in an non-trivial
spacetime geometry, which replaces the notion of gravitational field in this context.
Closed Geodesics:
Jacobi Fields and Comparison Theorems:
Euclidian space to Riemannian manifolds. A geodesic will be a constantly paramatrized,
smooth curve on the manifold, that is locally the shortest curve connecting two points with each other. They are of great importance in the further study of Riemannian Geometry, as well as in theoretical physics, in particular in
General Relativity, where they are the trajectories of test objects moving in an non-trivial
spacetime geometry, which replaces the notion of gravitational field in this context.
Closed Geodesics:
Jacobi Fields and Comparison Theorems:
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