Polar actions on irreducible compact Riemannian symmetric spaces have been studied by several authors. For some years, it has been a conjecture that the intersecting submanifold must always be flat if the space is of higher rank.
Very recently, this conjecture has been settled affirmatively. I will also talk about how one may use the duality of symmetric spaces to generalize this and similar results to the non-compact setting.
© Andreas Kollross.