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Dec 23, 2020 at 4:59 comment added Anton Petrunin If the dimension $\ge 3$, then geodesics almost never run in a convex hypersurface mathoverflow.net/a/8505. This statement is a bit stronger than nonexistence of geodesic surfaces in a generic manifold.
Jun 25, 2015 at 13:09 vote accept Uche Opara
Jun 20, 2015 at 14:11 history edited Robert Bryant CC BY-SA 3.0
Added some explicit criteria for the case n=3.
Jun 20, 2015 at 7:04 history edited Robert Bryant CC BY-SA 3.0
Added a missing condition
Jun 19, 2015 at 14:29 history answered Robert Bryant CC BY-SA 3.0