Levi-Civita connections for conformally deformed metrics on tame differential calculi

Article Type

Research Article

Publication Title

International Journal of Mathematics

Abstract

Given a tame differential calculus over a noncommutative algebra and an-bilinear metric g0, consider the conformal deformation g = k.g0, k being an invertible element of . We prove that there exists a unique connection on the bimodule of one-forms of the differential calculus which is torsionless and compatible with g. We derive a concrete formula connecting and the Levi-Civita connection for the metric g0. As an application, we compute the Ricci and scalar curvatures for a general conformal perturbation of the canonical metric on the noncommutative 2-Torus as well as for a natural metric on the quantum Heisenberg manifold. For the latter, the scalar curvature turns out to be a negative constant.

DOI

10.1142/S0129167X21500889

Publication Date

12-1-2021

Comments

Open Access, Green

This document is currently not available here.

Share

COinS