Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

Details Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

2008-01-27

arxiv.org/abs/0801.4127v1

Mathematics

Differential Geometry

23 pages, also contains two Maple worksheets and technical documentation

Scientific paper

10.1007/s10711-008-9297-2

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.

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