The index of exceptional symmetric spaces
Differential Geometry
2019-05-16 v1
Abstract
The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold (Onishchik, 1980). There is a conjecture by the first two authors for how to calculate the index. In this paper we give an affirmative answer to this conjecture for the exceptional Riemannian symmetric spaces and for the classical symmetric spaces Sp(r,R)/U(r). Our methodology is new and based on the idea of using slice representations for studying totally geodesic submanifolds.
Keywords
Cite
@article{arxiv.1905.06250,
title = {The index of exceptional symmetric spaces},
author = {Jürgen Berndt and Carlos Olmos and Juan Sebastián Rodríguez},
journal= {arXiv preprint arXiv:1905.06250},
year = {2019}
}
Comments
25 pages