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arXiv · 1905.09048

Laplace-Beltrami Operators on Noncommutative Tori

Hyunsu Ha·Raphael Ponge
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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.

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BibTeXRIS

Hyunsu Ha, Raphael Ponge. 2019-05-22. Laplace-Beltrami Operators on Noncommutative Tori. https://doi.org/10.1016/j.geomphys.2019.103594

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