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arXiv · 1707.04777

Einstein-Hilbert Action and on the Gauss-Bonnet Theorem for Riemannian Noncommutative Tori

Javad Golipour
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Abstract

We show the non-positivity of the Einstein-Hilbert action for conformal flat Riemannian metrics. The action vanishes only when the metric is constant flat. This recovers an earlier result of Fathizadeh-Khalkhali in the setting of spectral triples on noncommutative four-torus. Furthermore, computations of the gradient flow and the scalar curvature of this space based on modular operator are given. We also show the Gauss-Bonnet theorem for a parametrized class of non-diagonal metrics on noncommutative two-torus.

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Javad Golipour. 2017-07-15. Einstein-Hilbert Action and on the Gauss-Bonnet Theorem for Riemannian Noncommutative Tori. https://arxiv.org/abs/1707.04777

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