4 papers
Comparison of Levi-Civita connections in noncommutative geometry
Alexander Flamant, Bram Mesland, Adam Rennie
We compare the constructions of Levi-Civita connections for noncommutative algebras developed in arXiv:1505.07330, arXiv:1809.06721, arXiv:2403.13735. The assumptions in these vari…
Existence and uniqueness of the Levi-Civita connection on noncommutative differential forms
Bram Mesland, Adam Rennie
We combine Hilbert module and algebraic techniques to give necessary and sufficient conditions for the existence of an Hermitian torsion-free connection on the bimodule of differen…
Curvature and Weitzenbock formula for spectral triples
Bram Mesland, Adam Rennie
Using the Levi-Civita connection on the noncommutative differential one-forms of a spectral triple $(\B,\H,\D)$, we define the full Riemann curvature tensor, the Ricci curvature te…
Curvature and Weitzenbock formula for the PodleÅ quantum sphere
Bram Mesland, Adam Rennie
We prove that there is a unique Levi-Civita connection on the one-forms of the Dabrowski-Sitarz spectral triple for the PodleÅ sphere . We compute the full curvature te…