Can someone provide me exemples of connected Riemannian manifolds containing two points through each there are : (i) infinitely many geodesics (up to reparametrization) and (ii) no geodesics.
Thank you
2026-05-06 01:23:31.1778030611
Geodesics Examples
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Ok, so for (i) we can consider $S^{2}$ and for (ii) we can consider $\mathbb{R}^{n}\setminus\lbrace 0\rbrace$ (with Euclidian metric).
Thanks anyway and have a nice weekend :)