  We classify totally geodesic submanifolds in Hopf-Berger spheres, which
constitute a special family of homogeneous spaces diffeomorphic to spheres
constructed via Hopf fibrations. As a byproduct of our investigations, we have
discovered very intriguing examples of totally geodesic submanifolds. In
particular, we stand out the following three: totally geodesic submanifolds
isometric to real projective spaces, uncountably many isometric but
non-congruent totally geodesic submanifolds, and a totally geodesic submanifold
that is not extrinsically homogeneous. Remarkably, all these examples only
arise in certain Hopf-Berger spheres with positive curvature.
