量子射影空间的量子Riemannian geometry
Quantum Riemannian geometry of quantum projective spaces
摘要：
研究了任意维量子射影空间的量子黎曼几何。特别是我们计算的黎曼和里奇张量，使用以前介绍的量子度量和量子列维-奇维塔连接。我们证明了Riemann张量是双模映射，并推导出这一事实的各种后果。我们证明了Ricci张量与量子度规成正比，给出了爱因斯坦条件的量子模拟，并计算了相应的数量曲率。一路上，我们还证明了与这里提到的那些相关的各种对象的几个结果。
英文摘要：
We study the quantum Riemannian geometry of quantum projective spaces of any dimension. In particular we compute the Riemann and Ricci tensors, using previously introduced quantum metrics and quantum Levi-Civita connections. We show that the Riemann tensor is a bimodule map and derive various consequences of this fact. We prove that the Ricci tensor is proportional to the quantum metric, giving a quantum analogue of the Einstein condition, and compute the corresponding scalar curvature. Along the way we also prove several results for various objects related to those mentioned here.
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