Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram
نویسنده
چکیده
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. Author’s address. Sebastian Klein Department of Mathematics University College Cork Cork Ireland [email protected]
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