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Einstein-Hilbert Action and on the Gauss-Bonnet Theorem for Riemannian Noncommutative Tori. (arXiv:1707.04777v2 [math.DG] UPDATED)

来源于:arXiv
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. 查看全文>>