The Geometry of Compact Homogeneous Spaces with Two Isotropy Summands
نویسنده
چکیده
We give a complete list of all homogeneous spaces M = G/H where G is a simple compact Lie group, H a connected, closed subgroup, and G/H is simply connected, for which the isotropy representation of H on TpM decomposes into exactly two irreducible summands. For each homogeneous space, we determine whether it admits a G-invariant Einstein metric. When there is an intermediate subgroup H < K < G, we classify all the G-invariant Einstein metrics. This is an extension of the classification of isotropy irreducible spaces, given independently by O. V. Manturov [Ma1, Ma2, Ma3] and J. Wolf [Wo1, Wo2].
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