Extends Cartan calculus to H-equivariant braided geometries and proves existence/uniqueness of Levi-Civita connection for arbitrary pseudo-Riemannian metrics on such algebras.
Rosenberg, Levi-Civita’s Theorem for Noncommutative Tori , SIGMA, 9 (2013), 071
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Cartan structure equations and Levi-Civita connection in noncommutative geometry
Extends Cartan calculus to H-equivariant braided geometries and proves existence/uniqueness of Levi-Civita connection for arbitrary pseudo-Riemannian metrics on such algebras.