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



Existence of compact totally geodesic submanifold of codimension $1$
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.


