...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of the Mathematical Society of Japan >Geometry of weakly symmetric spaces
【24h】

Geometry of weakly symmetric spaces

机译：弱对称空间的几何

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Weakly symmetric spaces have been introduced by A. Selberg in 1956. His motivation was to generalize the Poisson summation formula to what is now known as the Selberg trace formula. These homogeneous spaces have the property that the differential operators which are invariant under the action of the full isometry group form a commutative algebra, that is, these spaces are commutative. Whereas much work has been done on the harmonic analysis of the commutative and weakly symmetric spaces, in particular on SL(2, R), the geometry of the weakly symmetric spaces has to our knowledge not been studied thoroughly. Only a few properties are given in [3]. The reason might be that Selberg's definition of weakly symmetric spaces appears to be rather abstract and only a few examples are known. The intention of this note is to point out that there is a nice geometrical characterizing property hidden in Selberg's definition leading to the construction of a whole list of new examples, and to stimulate further research on the Riemannian geometry of this class of spaces.
机译：弱对称空间由A. Selberg在1956年提出。他的动机是将Poisson和公式推广为现在称为Selberg跟踪公式。这些齐次空间的性质是，在全等轴测图群的作用下不变的微分算子形成一个可交换的代数，即这些空间是可交换的。尽管在交换和弱对称空间，尤其是SL（2，R）的谐波分析上已经做了大量工作，但据我们所知，对弱对称空间的几何形状还没有进行深入研究。 [3]中仅给出了一些属性。原因可能是Selberg对弱对称空间的定义似乎很抽象，并且只有几个例子是已知的。本说明的目的是指出，Selberg定义中隐藏了一个不错的几何特征，从而构造了一系列新示例，并激发了对此类空间的黎曼几何的进一步研究。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号