Classification of invariant Einstein metrics on certain compact homogeneous spaces
Classification of invariant Einstein metrics on certain compact homogeneous spaces
复制标题
某些紧齐次空间上不变爱因斯坦度量的分类
DOI：
10.1007/s11425-018-9357-1
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Deng Shaoqiang
中科院分区：
文献类型：
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作者：
Yan Zaili;Chen Huibin;Deng Shaoqiang
In this paper, we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands. We show that, ifG/Kis a compact isotropy irreducible space withGandKsimple, then except for some very special cases, the coset spaceG×G=Δ(K) carries at least two invariant Einstein metrics. Furthermore, in the case thatG1;G2andKare simple Lie groups, withK⊂G1;K⊂G2, andG1≠G2, such thatG1/KandG2/Kare compact isotropy irreducible spaces, we give a complete classification of invariant Einstein metrics on the coset spaceG1×G2=Δ(K).
