非交换环上函数度量的谱几何学

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-07 DOI:10.4310/cntp.2024.v18.n1.a4

Asghar Ghorbanpour, Masoud Khalkhali

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引用次数: 0

摘要

我们在非交换环上引入了一类新的度量，称为函数度量，并研究了它们的谱几何。我们为这些度量定义了一类拉普拉斯型算子，并研究了从热轨迹渐近得到的它们的谱不变式。我们得到了热轨迹的第二密度公式。特别是，对于某些类型的度量，包括保角平坦度量和平坦度量的扭曲乘积，在所有维度上都明确计算了函数度量的标量曲率密度和总标量曲率。最后，证明了配备一般功能度量的非交换二环面的高斯-波内特定理。

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Spectral geometry of functional metrics on noncommutative tori

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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.