Symmetric Spaces with Rectangular Unit Lattices, Revisited
Differential Geometry
2025-09-22 v1
Abstract
We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean space which reveals X as a standardly embedded symmetric R-space. We further determine the root systems, Euclidean root data, fundamental groups and eigenvalues of the Laplacian of symmetric spaces with rectangular unit lattice in a direct way.
Cite
@article{arxiv.2509.16166,
title = {Symmetric Spaces with Rectangular Unit Lattices, Revisited},
author = {Jost-Hinrich Eschenburg and Ernst Heintze and Peter Quast},
journal= {arXiv preprint arXiv:2509.16166},
year = {2025}
}