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May 13, 2021 at 15:33 vote accept Nate River
May 13, 2021 at 14:31 answer added Leo Moos timeline score: 3
May 13, 2021 at 9:16 comment added Nate River Wouldn’t $\{v\}$ have null measure though?
May 13, 2021 at 9:15 comment added David Hughes Your condition implies all geodesics are closed - let $K = \{ v \}$ for some $v \in T_p M \setminus \{0\}$ - so the distance function on $M$ is bounded and hence, $M$ must be compact.
May 13, 2021 at 8:28 history edited Nate River CC BY-SA 4.0
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May 13, 2021 at 8:23 history edited Nate River CC BY-SA 4.0
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May 13, 2021 at 8:10 history asked Nate River CC BY-SA 4.0