I'm doing a project exploring Riemannian immersions and submersions. In O'Neil's book, Semi-Riemannian Geometry, he mentions umbilic points and totally umbilic hypersurfaces and proves some interesting results.
I'm wondering if there is are any other good treatments of umbilic points and totally umbilic hypersurfaces, preferably in a Riemannian context rather than a Semi-Riemannian context.