Sectional curvatures and quasisymmetric domains
Sectional curvatures and quasisymmetric domains
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截面曲率和拟对称域
DOI：
10.4310/jdg/1214435985
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发表时间：
1981
影响因子：
2.5
通讯作者：
J. D'Atri
中科院分区：
文献类型：
--
作者：
J. D'Atri
本文继续研究了正规y-代数上由可容许形式产生的齐次Kahler度量的曲率性质[1]，[2]。众所周知，这类包括齐次有界域上的Bergman度量。在§1中，我们导出了非正截面曲率的新的必要条件。然后在§2中，我们利用这些结果和J. Dorfmeister[3]的结果来证明我们的主要结果：如果一个拟对称定义域（在Satake[6]意义上）在Bergman度规中具有非正的截面曲率，那么它是对称的。这应该与Zelow (Lundquist)[7]，[8]的结果形成对比，即准对称区域具有全纯截面曲率，其边界上有一个负常数。§3给出了[2]结果的改进和修正。
This paper continues our study [1], [2] of the curvature properties of the class of homogeneous Kahler metrics arising from admissible forms on normal y-algebras. As is well-known, this class includes the Bergman metrics on homogeneous bounded domains. In § 1 we derive new necessary conditions for nonpositive sectional curvature. Then in §2 we use these and the results of J. Dorfmeister [3] to prove our main result: If a quasi-symmetric domain (in the sense of Satake [6]) has nonpositive sectional curvature in the Bergman metric, then it is symmetric. This should be contrasted with the result of Zelow (Lundquist) [7], [8] that quasi-symmetric domains have holomorphic sectional curvature bounded above by a negative constant. §3 gives an improvement of a result in [2] and a correction.