Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram
Abstract
The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.
Keywords
Cite
@article{arxiv.0801.4127,
title = {Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram},
author = {Sebastian Klein},
journal= {arXiv preprint arXiv:0801.4127},
year = {2008}
}
Comments
23 pages, also contains two Maple worksheets and technical documentation