Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 079, 21 pages      arXiv:1803.04036      https://doi.org/10.3842/SIGMA.2018.079

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

Leonard Huang
Department of Mathematics, University of Colorado at Boulder, Campus Box 395, 2300 Colorado Avenue, Boulder, CO 80309-0395, USA

Received March 13, 2018, in final form July 21, 2018; Published online July 29, 2018

Abstract
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.

Key words: quantum torus; generically transcendental; quantum metric space; metrized quantum vector bundle; Riemannian metric; Levi-Civita connection.

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