Gauss-Bonnet for matrix conformally rescaled Dirac

Abstract

We derive an explicit formula for the scalar curvature over a two-torus with a Dirac operator conformally rescaled by a globally diagonalizable matrix. We show that the Gauss-Bonnet theorem holds and extend the result to all Riemann surfaces with Dirac operators modified in the same way.

10 pages

References in corpus (9)

• The Gauss-Bonnet Theorem for the noncommutative two torus
• On the Gauss-Chern-Bonnet theorem for the noncommutative 4-sphere
• The term a_4 in the heat kernel expansion of noncommutative tori
• Twisted reality condition for Dirac operators
• Heat trace for Laplacian type operators with non-scalar symbols
• On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for $C^{\ast }$-Dynamical Systems
• A Scalar Curvature Formula For the Noncommutative 3-Torus
• On Certain Spectral Invariants of Dirac Operators on Noncommutative Tori
• The Moyal Sphere

Cited by in corpus (2)

• Laplace-Beltrami Operators on Noncommutative Tori
• Levi-Civita connections from toral actions