Geodesic
On Quotient Spaces of Compact Lie Groups by Tori Centralizers
Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 293-304.

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We consider the graph of the homogeneous space $K/L$, where $K$ is a compact Lie group and $L$ is the centralizer of a torus in $K$. We obtain a characterization of those spaces whose graphs admit embeddings in a certain standard graph. We compute the number of arcs in such graphs. We also give a simple expression for the Euler class of the homogeneous space $K/L$.
Keywords: homogeneous space, root system, simple root, graph of a root system
Mots-clés : Euler class. 
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A. N. Shchetinin. On Quotient Spaces of Compact Lie Groups by Tori Centralizers. Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 293-304. http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a12/

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