The Moyal Sphere

Abstract

We construct a family of constant curvature metrics on the Moyal plane and compute the Gauss-Bonnet term for each of them. They arise from the conformal rescaling of the metric in the orthonormal frame approach. We find a particular solution, which corresponds to the Fubini-Study metric and which equips the Moyal algebra with the geometry of a noncommutative sphere.

16 pages, 3 figures

References in corpus (2)

• A Gravity Theory on Noncommutative Spaces
• The Gauss-Bonnet Theorem for the noncommutative two torus

Cited by in corpus (5)

• On the Gauss-Chern-Bonnet theorem for the noncommutative 4-sphere
• Spectral dimensions and dimension spectra of quantum spacetimes
• A Scalar Curvature Formula For the Noncommutative 3-Torus
• Gauss-Bonnet for matrix conformally rescaled Dirac
• Curvature, area and Gauss-Bonnet formula of the Moyal sphere