We consider homogeneous spaces G/K with G a simple compact Lie group, endowed with an arbitrary G-invariant Riemannian metric. We classify those spaces where the action of K on G/K is polar and show that such spaces are locally symmetric. Moreover we give a classification of pairs (G, K) with G compact semisimple such that K has polar linear isotropy representation.
Homogeneous spaces with polar isotropy / F. PODESTA'; A. KOLLROSS. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 110:(2003), pp. 487-503. [10.1007/s00229-002-0345-1]
Homogeneous spaces with polar isotropy
PODESTA', FABIO;
2003
Abstract
We consider homogeneous spaces G/K with G a simple compact Lie group, endowed with an arbitrary G-invariant Riemannian metric. We classify those spaces where the action of K on G/K is polar and show that such spaces are locally symmetric. Moreover we give a classification of pairs (G, K) with G compact semisimple such that K has polar linear isotropy representation.
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