Abstract We ask a general question: what are locally homogeneous compact pseudo-Riemannian Einstein manifolds? We show that any standard compact Clifford–Klein form of a simple non-compact Lie group admits at least one Einstein metric. We conjecture that these are basically the only possible locally homogeneous Einstein Riemannian compact manifolds using T. Kobayashi’s conjecture as a guiding principle.

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关于局部齐次拟黎曼紧致爱因斯坦流形

摘要 我们提出一个普遍的问题：什么是局部齐次紧拟黎曼爱因斯坦流形？我们证明了简单非紧李群的任何标准紧致 Clifford-Klein 形式都承认至少一个爱因斯坦度量。我们以小林小林猜想为指导原则，推测这些基本上是唯一可能的局部齐次爱因斯坦黎曼紧流形。