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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University College Cork, Cork, Ireland

    Sebastian Klein

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  1. Sebastian Klein
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Correspondence to Sebastian Klein.

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Klein, S. Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram. Geom Dedicata 138, 25–50 (2009). https://doi.org/10.1007/s10711-008-9297-2

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  • DOI: https://doi.org/10.1007/s10711-008-9297-2

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