HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH FIVE ISOTROPY SUMMANDS
HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH FIVE ISOTROPY SUMMANDS
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DOI：
10.1142/s0129167x13500778
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发表时间：
2012-07
影响因子：
0.6
通讯作者：
A. Arvanitoyeorgos;I. Chrysikos;Y. Sakane
中科院分区：
文献类型：
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作者：
A. Arvanitoyeorgos;I. Chrysikos;Y. Sakane
我们构造了紧致单李群G的广义旗流形G/K的齐次Einstein方程，G的各向同性表示分解为五个不等价的不可约Ad（K）-子模.为此，我们采用了一种新的技术，这是基于纤维化的旗流形在另一个这样的空间和理论的黎曼淹没。我们分类所有广义旗流形与五个各向同性和，我们使用Grobner基地研究相应的多项式系统的爱因斯坦方程。对于广义旗流形E6/（SU（4）× SU（2）× U（1）× U（1））和E7/（U（1）× U（6）），我们明确地找到了直到等距的所有不变Einstein度量.对于广义旗流形SO（2l + 1）/（U（1）× U（p）× SO（2（l-p- 1）+ 1））和SO（2l）/（U（1）× U（p）× SO（2（l-p- 1），我们证明了至少两个非Kahler-Einstein度量的存在性.对于较小的l和p值，我们给出了不变爱因斯坦度量的精确数目。
We construct the homogeneous Einstein equation for generalized flag manifolds G/K of a compact simple Lie group G whose isotropy representation decomposes into five inequivalent irreducible Ad(K)-submodules. To this end, we apply a new technique which is based on a fibration of a flag manifold over another such space and the theory of Riemannian submersions. We classify all generalized flag manifolds with five isotropy summands, and we use Grobner bases to study the corresponding polynomial systems for the Einstein equation. For the generalized flag manifolds E6/(SU(4) × SU(2) × U(1) × U(1)) and E7/(U(1) × U(6)) we find explicitly all invariant Einstein metrics up to isometry. For the generalized flag manifolds SO(2l + 1)/(U(1) × U(p) × SO(2(l - p - 1) + 1)) and SO(2l)/(U(1) × U(p) × SO(2(l - p - 1))) we prove existence of at least two non-Kahler–Einstein metrics. For small values of l and p we give the precise number of invariant Einstein metrics.