论文标题
离散圆和圆环的Riemannian几何形状
Riemannian Geometry of a Discretized Circle and Torus
论文作者
论文摘要
我们将Riemannian几何形状的结果扩展到有限基团上，并为有限的环状基团上最小的非交通差分积分提供了所有线性连接的完整分类。我们一般可以解决无扭转和度量的兼容性条件，并表明有几类的解决方案，其中只有特殊的解决方案与一个指标兼容，该指标在单一形式的空间上提供了Hilbert $ c^\ ast $模块结构。我们为这些指标计算曲率和标态曲率，并找到它们的连续限制。
We extend the results of Riemannian geometry over finite groups and provide a full classification of all linear connections for the minimal noncommutative differential calculus over a finite cyclic group. We solve the torsion-free and metric compatibility condition in general and show that there are several classes of solutions, out of which only special ones are compatible with a metric that gives a Hilbert $C^\ast$-module structure on the space of the one-forms. We compute curvature and scalar curvature for these metrics and find their continuous limits.
