In [Zeghib: Laminations et hypersurfaces géodésiques des variétés hyperboliques, Annales scientifiques de l'ENS, 1991] it is shown, that in a compact manifold of negative curvature, there exists only a finite number of totally geodesic hypersurfaces (codim=1) without self-intersections.
Now my question: Is there an example of such a compact manifold M (with dim(M) > 2) , that allows even one totally geodesique hypersurface? Or a result that proofs the existence?
In manifolds of variable curvature it is not clear, that there exists even one totally geodesic hypersurface.
In the case of constant curvature it is clear in the universal covering (hyperbolic space), bur for a compact manifold?