Geodesic
Highly Symmetric Homogeneous Spaces
Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 291-293

Voir la notice de l'article provenant de la source Cambridge University Press

We consider effective homogeneous spaces M = G/H where G is a compact connected Lie group, H is a closed subgroup and G acts effectively on M (i.e., H contains no non-trivial subgroup normal in G). It is known that dim G ≦ m 2/2 + m/2 where m = dim M and that if dim G = m 2/2 + m/2, then M is diffeomorphic to the standard sphere Sm or the standard real projective space RPm [1]. In addition it has been shown that for fixed m there are gaps in the possible dimensions for G below the maximal bound [4; 5]. 
Mann, L. N. Highly Symmetric Homogeneous Spaces. Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 291-293. doi: 10.4153/CJM-1974-030-0
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[5] 5. Mann, L. N., Further gaps in the dimensions of transformation groups, Illinois J. Math. 15 (1969), 740–756. Google Scholar

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