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Results tagged with closed-geodesic
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user 1441
8
votes
1
answer
490
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Metrics on torus without closed contractible geodesics
It is easy to see that any closed geodesic on a flat 2-torus is noncontractible.
Further the same holds true for a torus of revolution.
Indeed either a closed geodesic is a meridian and therefore non …
- 45k
24
votes
3
answers
1k
views
A problem on Gauss--Bonnet formula
While teaching a course in differential geometry, I came up with the following problem, which I think is cool.
Assume $\gamma$ is a closed geodesic on a sphere $\Sigma$ with positive Gauss curvature.
…
- 45k