Levi-Civita connections and vector fields for noncommutative differential calculi

DOI10.1142/S0129167X20500652OpenAlexW3101840861MaRDI QIDQ5130960

Jyotishman Bhowmick, Debashish Goswami, Giovanni Landi

Publication date: 31 October 2020

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.01545

zbMATH Keywords

noncommutative geometryLevi-Civita connectioncovariant derivativeKoszul formula

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Noncommutative geometry (à la Connes) (58B34) Connections (general theory) (53C05) Other connections (53B15)

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Levi-Civita connections on quantum spheres, Gauge theories on quantum spaces, A new look at Levi-Civita connection in noncommutative geometry, Levi-Civita connections on braided algebras, On the Koszul formula in noncommutative geometry, Riemannian geometry of a discretized circle and torus, Levi-Civita connections for conformally deformed metrics on tame differential calculi

Cites Work

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• Supersymmetric quantum theory and non-commutative geometry
• Levi-Civita connections on the quantum groups \(SL_ q(N), O_ q(N)\) and \(Sp_ q(N)\)
• Connections on central bimodules in noncommutative differential geometry
• Levi-Civita connections for a class of spectral triples
• Scalar curvature of a Levi-Civita connection on the Cuntz algebra with three generators
• Riemannian curvature of the noncommutative 3-sphere
• Braided Cartan calculi and submanifold algebras
• Levi-Civita's theorem for noncommutative tori
• On noncommutative Levi-Civita connections
• Vector Bundles and Gromov–Hausdorff Distance
• On the Koszul formula in noncommutative geometry
• Quantum Riemannian Geometry
• Metrics and pairs of left and right connections on bimodules