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3
votes
Accepted
Infinite number of closed geodesics on distorted sphere
Will Jagy answered my question:
Bangert, Victor. "On the existence of closed geodesics on two-spheres." International Journal of Mathematics 4, no. 01 (1993): 1-10.
doi.
"...one obtains the existenc …
3
votes
Is there the longest geodesic?
This seems relevant to your question.
An isosceles tetrahedron (all four faces congruent)
contains arbitrarily long closed simple geodesics.
This paper proves the reverse: having such geodesics implie …