7 citations · 22 across the 6 of their papers we have counts for
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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…
On inductive limit spectral triples
Remus Floricel, Asghar Ghorbanpour
Given an inductive system of spectral triples $\{(A_j,\H_j,D_j)\}_j$, we find conditions under which the triple $(\limind A_j,\limind H_j,\limind D_j)$ is a spectral triple. We als…
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…
The Curvature of the Determinant Line Bundle on the Noncommutative Two Torus
Ali Fathi, Asghar Ghorbanpour, Masoud Khalkhali
We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surface…