由有限代数产生的非正曲率空间
Spaces of nonpositive curvature arising from a finite algebra
摘要：
在本文中，我们引入了一族例子，它们可以被视为非正曲率空间，但具有不同的性质，即它们作为度量空间是不完备的。这相当于这样一个事实，即它们是在有限冯诺依曼代数上建模的，并且引入的度量来自代数的迹。尽管这些流形的不完备性，它们的几何可以从度量几何的观点来研究，并从泛函分析中得到的几种技术被应用于洞察它们的测地线结构。
英文摘要：
In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are modelled on a finite von Neumann algebra, and the metrics introduced arise from the trace of the algebra. In spite of the noncompleteness of these manifolds, their geometry can be studied from the view-point of metric geometry, and several techniques derived from the functional analysis are applied to gain insight on their geodesic structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
