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Mikhail Katz
Mikhail Katz
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For a homogeneous metric there is no reason for a geodesic loop at a point to be necessarily a closed geodesic. Counterexamples can probably be constructed already using metrics on the 3-sphere constructed by rescaling the round metric along the fiber of the Hopf fibration.

For a homogeneous metric there is no reason for a geodesic loop at a point to be necessarily a closed geodesic. Counterexamples can probably be constructed already using metrics on the 3-sphere constructed by rescaling the metric along the fiber of the Hopf fibration.

For a homogeneous metric there is no reason for a geodesic loop at a point to be necessarily a closed geodesic. Counterexamples can probably be constructed already using metrics on the 3-sphere constructed by rescaling the round metric along the fiber of the Hopf fibration.

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Mikhail Katz
Mikhail Katz
  • 16.6k
  • 2
  • 54
  • 127

For a homogeneous metric there is no reason for a geodesic loop at a point to be necessarily a closed geodesic. Counterexamples can probably be constructed already using metrics on the 3-sphere constructed by rescaling the metric along the fiber of the Hopf fibration.