论文标题
紧凑的对称空间的稳定性
Stability of Compact Symmetric Spaces
论文作者
论文摘要
在本文中，我们研究了爱因斯坦 - 希尔伯特（Einstein-Hilbert）在紧凑型对称空间上的稳定性问题，并完成了考索（Koiso）对该受试者的开创性工作。我们详细介绍了与casimir特征值的简单谎言代数的不可约合表示，而不是伴随表示的Casimir特征值，并使用此信息来证明Quaternionic和Cayley Project partivice平面对Einstein指标的稳定性。此外，我们证明了关于季气格拉曼尼亚人与投影空间不同的爱因斯坦指标是不稳定的。
In this article we study the stability problem for the Einstein-Hilbert functional on compact symmetric spaces following and completing the seminal work of Koiso on the subject. We classify in detail the irreducible representations of simple Lie algebras with Casimir eigenvalue less than the Casimir eigenvalue of the adjoint representation, and use this information to prove the stability of the Einstein metrics on both the quaternionic and Cayley projective plane. Moreover we prove that the Einstein metrics on quaternionic Grassmannians different from projective spaces are unstable.
