Totally geodesic submanifolds in exceptional symmetric spaces
Differential Geometry
2023-02-24 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2202.10775,
title = {Totally geodesic submanifolds in exceptional symmetric spaces},
author = {Andreas Kollross and Alberto Rodríguez-Vázquez},
journal= {arXiv preprint arXiv:2202.10775},
year = {2023}
}
Comments
Accepted for publication in Advances in Mathematics