Spectral geometry of functional metrics on noncommutative tori
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866910440733278208 |
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| author | Ghorbanpour, Asghar Khalkhali, Masoud |
| author_facet | Ghorbanpour, Asghar Khalkhali, Masoud |
| contents | We introduce a new family of metrics, called functional metrics, on noncommutative tori and study their spectral geometry. We define a class of Laplace type operators for these metrics and study their spectral invariants obtained from the heat trace asymptotics. A formula for the second density of the heat trace is obtained. In particular, the scalar curvature density and the total scalar curvature of functional metrics are explicitly computed in all dimensions for certain classes of metrics including conformally flat metrics and twisted product of flat metrics. Finally a Gauss-Bonnet type theorem for a noncommutative two torus equipped with a general functional metric is proved. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1811_04004 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Spectral geometry of functional metrics on noncommutative tori Ghorbanpour, Asghar Khalkhali, Masoud Quantum Algebra Mathematical Physics Differential Geometry Operator Algebras Spectral Theory 58B34 (Primary), 46L87, 58J42 (Secondary) We introduce a new family of metrics, called functional metrics, on noncommutative tori and study their spectral geometry. We define a class of Laplace type operators for these metrics and study their spectral invariants obtained from the heat trace asymptotics. A formula for the second density of the heat trace is obtained. In particular, the scalar curvature density and the total scalar curvature of functional metrics are explicitly computed in all dimensions for certain classes of metrics including conformally flat metrics and twisted product of flat metrics. Finally a Gauss-Bonnet type theorem for a noncommutative two torus equipped with a general functional metric is proved. |
| title | Spectral geometry of functional metrics on noncommutative tori |
| topic | Quantum Algebra Mathematical Physics Differential Geometry Operator Algebras Spectral Theory 58B34 (Primary), 46L87, 58J42 (Secondary) |
| url | https://arxiv.org/abs/1811.04004 |