The geometry of compact homogeneous spaces with two isotropy summands |
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Authors: | William Dickinson Megan M Kerr |
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Institution: | (1) Department of Mathematics, Grand Valley State University, 2307 Mackinac Hall, Allendale, MI 49401, USA;(2) Department of Mathematics, Wellesley College, 106 Central St., Wellesley, MA 02481, USA |
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Abstract: | 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 T
p
M 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 Manturov (Dokl. Akad. Nauk SSSR 141, (1961), 792–795 1034–1037, Tr. Semin. Vector Tensor Anal. 13, (1966), 68–145) and J Wolf (Acta Math. 120, (1968), 59–148 152, (1984) 141–142).
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Keywords: | Homogeneous spaces Isotropy representation Einstein metrics |
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