Geometriae Dedicata

, Volume 138, Issue 1, pp 25–50 | Cite as

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

Original Paper
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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 its Satake diagram, in a way that is suited for the use with computer algebra systems; an example implementation for Maple Version 10 can be found on http://satake.sourceforge.net. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.

Keywords

Satake diagram Structure constants Chevalley constants Curvature tensor Riemannian symmetric space 

Mathematics Subject Classification (2000)

53C35 53B20 17B20 17-08 
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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College CorkCorkIreland

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