论文标题
Fubini研究指标和量子射击空间上的Levi-Civita连接
Fubini-Study metrics and Levi-Civita connections on quantum projective spaces
论文作者
论文摘要
我们介绍了Fubini-study指标的类似物以及量子射击空间上相应的Levi-Civita连接。我们将量子指标定义为两张量，从适当的意义上讲，就Heckenberger和Kolb引入的差分计算而言。我们在这些结石上定义了连接，并表明它们是无扭转和不含扭转的连接，后者条件使用量子公制，并且是度量兼容性的较弱概念。最后，我们证明这些连接是双模型连接，并且指标兼容性也具有更强的意义。
We introduce analogues of the Fubini-Study metrics and the corresponding Levi-Civita connections on quantum projective spaces. We define the quantum metrics as two-tensors, symmetric in the appropriate sense, in terms of the differential calculi introduced by Heckenberger and Kolb. We define connections on these calculi and show that they are torsion free and cotorsion free, where the latter condition uses the quantum metric and is a weaker notion of metric compatibility. Finally we show that these connections are bimodule connections and that the metric compatibility also holds in a stronger sense.
