Laplace-Beltrami Operators on Noncommutative Tori
arXiv:1905.09048 · doi:10.1016/j.geomphys.2019.103594
Abstract
In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian manifolds. The construction takes into account the non-triviality of the group of modular automorphisms. On the way we introduce notions of Riemannian density and Riemannian volumes for noncommutative tori.
v2: typos have been fixed. New normalization of Riemannian volume. To appear in J. Geom. Phys., 28 pages