On the index of symmetric spaces - Olmos, Carlos Enrique (2018)
Let M be an irreducible Riemannian symmetric space. The indexof M is the minimal codimension of a (non-trivial) totally geodesic submanifoldof M. We prove that the index is bounded from below by the rank ofthe symmetric space. We also classify the irreducible Riemannian symmetricspaces whose index is less or equal than 3.