Is there a compact orientable Riemannian manifold which does not have a compact totally geodesic submanifold of codimension $1$?
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asked Mar 31, 2019 at 23:51
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1 Answer
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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.
answered Apr 1, 2019 at 1:23
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$\begingroup$ Thank you very much for your answer. $\endgroup$ Commented Apr 1, 2019 at 2:21