2022/02/22 by Andreas Kollross, Kollross, Andreas, Alberto Rodríguez-Vázquez +1
Mathematics · #Geometry and complex manifolds #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2202.10775
We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We prove a result analogous to the index conjecture: for every irreducible symmetric space of non-compact type, there exists a totally geodesic submanifold which is of minimal codimension and whose non-flat irreducible factors have Dynkin index equal to one.