On the volume of orbifold quotients of symmetric spaces
On the volume of orbifold quotients of symmetric spaces
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DOI：
10.1016/j.difgeo.2020.101639
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发表时间：
2018-08
影响因子：
0.5
通讯作者：
Ilesanmi Adeboye;Mckenzie Y. Wang;Guofang Wei
中科院分区：
文献类型：
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作者：
Ilesanmi Adeboye;Mckenzie Y. Wang;Guofang Wei
H.C. Wang 对非紧半单李群 Zassenhaus 邻域的定量研究的关键是两个常数，它们取决于相应李代数的根系。本文将 Wang 常数的值列表扩展到异常李群，并消除了它们对维数的依赖。第一个应用是半简单李群上的规范左不变度量的改进的上截面曲率界。第二个应用是给定的非紧型不可约对称空间的任意轨道商的显式一致正下界。
Key to H. C. Wang's quantitative study of Zassenhaus neighbourhoods of non-compact semisimple Lie groups are two constants that depend on the root system of the corresponding Lie algebra. This article extends the list of values for Wang's constants to the exceptional Lie groups and also removes their dependence on dimension. The first application is an improved upper sectional curvature bound for a canonical left-invariant metric on a semisimple Lie group. The second application is an explicit uniform positive lower bound for arbitrary orbifold quotients of a given irreducible symmetric space of non-compact type.