The Ricci flow on noncommutative two-tori

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.

18 pages, LaTeX

References in corpus (12)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci Flow and the Poincare Conjecture
• Ricci flow and black holes
• The Gauss-Bonnet Theorem for the noncommutative two torus
• Noncommutative BTZ Black Hole and Discrete Time
• Quantum Statistical Mechanics, L-series and Anabelian Geometry
• Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture
• Noncommutative BTZ Black Hole in Polar Coordinates
• Eigenvalues of the Laplacian under the Ricci Flow
• Zeta functions that hear the shape of a Riemann surface
• A noncommutative sigma-model

Cited by in corpus (15)

• Curved noncommutative torus and Gauss--Bonnet
• An Asymmetric Noncommutative Torus
• The term a_4 in the heat kernel expansion of noncommutative tori
• Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds
• A Riemann-Roch theorem for the noncommutative two torus
• Weyl's Law and Connes' Trace Theorem for Noncommutative Two Tori
• On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for $C^{\ast }$-Dynamical Systems
• Noncommutative Ricci flow in a matrix geometry
• Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals
• On Certain Spectral Invariants of Dirac Operators on Noncommutative Tori
• Hypergeometric function and Modular Curvature II. Connes-Moscovici functional relation after Lesch's work
• Pseudodifferential calculus on noncommutative tori, II. Main properties
• The Curvature of the Determinant Line Bundle on the Noncommutative Two Torus
• Analyticity and spectral properties of noncommutative Ricci flow in a matrix geometry
• A twisted local index formula for curved noncommutative two tori