Closed geodesics and orthogonal geodesic chords without self-intersections

  • Hans-Bert Rademacher (Leipzig University)
E2 10 (Leon-Lichtenstein)


We show that for a generic Riemannian metric on a compact manifold of dimension at least three all closed geodesics do not have self-intersections. Similar results are possible for geodesic loops and orthogonal geodesic chords. An orthogonal geodesic chord on a manifold with boundary is a geodesic segment connecting points on the boundary and hitting the boundary orthogonally.

Antje Vandenberg

MPI for Mathematics in the Sciences Contact via Mail

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