The Index Conjecture for Symmetric Spaces (2003.01393v3)

Abstract: In 1980, Onishchik introduced the index of a Riemannian symmetric space as the minimal codimension of a (proper) totally geodesic submanifold. He calculated the index for symmetric spaces of rank less than or equal to 2, but for higher rank it was unclear how to tackle the problem. In earlier papers we developed several approaches to this problem, which allowed us to calculate the index for many symmetric spaces. Our systematic approach led to a conjecture for how to calculate the index. The purpose of this paper is to verify the conjecture.