Laplace-Beltrami operators on noncommutative tori

JOURNAL OF GEOMETRY AND PHYSICS

卷:150

Article

Ha, Hyunsu¹  Ponge, Raphael² 

[1] Seoul Natl Univ, Dept Math Sci, Seoul, South Korea

[2] Sichuan Univ, Sch Math, Chengdu, Peoples R China

关键词: Noncommutative tori;    Riemannian metrics;    Laplace-Beltrami operator;   

DOI  :  10.1016/j.geomphys.2019.103594

来源: Elsevier

【 摘 要 】

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 on noncommutative tori. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free