The Ricci flow on noncommutative two-tori

TL;DR

This paper develops a Ricci flow framework for noncommutative two-tori using spectral methods and recent geometric results, extending classical geometric analysis to noncommutative geometry.

Contribution

It introduces a spectral formulation of Ricci flow tailored for noncommutative 2-tori, leveraging eigenvalues, eigenfunctions, and noncommutative Gauss-Bonnet theorem insights.

Findings

Constructed a spectral Ricci flow model for noncommutative tori

Extended classical geometric flow concepts to noncommutative geometry

Connected spectral properties with geometric invariants in noncommutative setting

Abstract

In this paper we construct a version of Ricci flow for noncommutative 2-tori, based on a spectral formulation in terms of the eigenvalues and eigenfunction of the Laplacian and recent results on the Gauss-Bonnet theorem for noncommutative tori.