Is there a compact orientable Riemannian manifold which does not have a compact totally geodesic submanifold of codimension $1$?


1 Answer 1


According to the answer of Petrunin https://mathoverflow.net/a/309692/121665, any metric on a 3-manifold admits arbitrary small $C^\infty$ deformation such that the obtained Riemannian manifold has no totally geodesic surfaces, even locally.

  • $\begingroup$ Thank you very much for your answer. $\endgroup$ Apr 1, 2019 at 2:21

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