Metrized Quantum Vector Bundles over Quantum Tori Built from Riemannian Metrics and Rosenberg's Levi-Civita Connections

Symmetry Integrability and Geometry-Methods and Applications

article

Leonard Huang¹ 

[1] Department of Mathematics, University of Colorado at Boulder, Campus Box 395

关键词: quantum torus;    generically transcendental;    quantum metric space;    metrized quantum vector bundle;    Riemannian metric;    Levi-Civita connection;   

DOI  :  10.3842/SIGMA.2018.079

来源: National Academy of Science of Ukraine

【 摘 要 】

We build metrized quantum vector bundles, over a generically transcendental quantum torus, from Riemannian metrics, using Rosenberg's Levi-Civita connections for these metrics. We also prove that two metrized quantum vector bundles, corresponding to positive scalar multiples of a Riemannian metric, have distance zero between them with respect to the modular Gromov-Hausdorff propinquity.

【 授权许可】

Unknown