Existence of compact totally geodesic submanifold of codimension $1$

Question

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

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.