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.
arXiv commentv2: typos have been fixed. New normalization of Riemannian volume. To appear in J. Geom. Phys., 28 pages
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- Semiclassical Weyl law and exact spectral asymptotics in noncommutative geometry
- Local invariants of non-commutative tori
- Connes Trace Theorem for Curved Noncommutative Tori. Application to Scalar Curvature
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- Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger Operators on Curved Noncommutative Tori
- General Rearrangement Lemma for Heat Trace Asymptotic on Noncommutative Tori
- Levi-Civita connections from toral actions