45 citations · 323 across the 58 of their papers we have counts for
27 papers · 1 filter
Curvature in Noncommutative Geometry
Farzad Fathizadeh, Masoud Khalkhali
Our understanding of the notion of curvature in a noncommutative setting has progressed substantially in the past ten years. This new episode in noncommutative geometry started whe…
Spectral geometry of functional metrics on noncommutative tori
Asghar Ghorbanpour, Masoud Khalkhali
We introduce a new family of metrics, called functional metrics, on noncommutative tori and study their spectral geometry. We define a class of Laplace type operators for these met…
The Ricci Curvature for Noncommutative Three Tori
Rui Dong, Asghar Ghorbanpour, Masoud Khalkhali
We compute the Ricci curvature of a curved noncommutative three torus. The computation is done both for conformal and non-conformal perturbations of the flat metric. To perturb the…
Gauss-Bonnet for matrix conformally rescaled Dirac
Masoud Khalkhali, Andrzej Sitarz
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-Bonne…
The Ricci Curvature in Noncommutative Geometry
Remus Floricel, Asghar Ghorbanpour, Masoud Khalkhali
Motivated by the local formulae for asymptotic expansion of heat kernels in spectral geometry, we propose a definition of Ricci curvature in noncommutative settings. The Ricci oper…
On Certain Spectral Invariants of Dirac Operators on Noncommutative Tori
Ali Fathi, Masoud Khalkhali
The spectral eta function for certain families of Dirac operators on noncommutative -torus is considered and the regularity at zero is proved. By using variational techniques, w…