# Spectral geometry of functional metrics on noncommutative tori

@article{Ghorbanpour2018SpectralGO, title={Spectral geometry of functional metrics on noncommutative tori}, author={Asghar Ghorbanpour and Masoud Khalkhali}, journal={arXiv: Quantum Algebra}, year={2018} }

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…

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