Corpus ID: 55226642

A new look at Levi-Civita connection in noncommutative geometry

@article{Bhowmick2016ANL,
  title={A new look at Levi-Civita connection in noncommutative geometry},
  author={J. Bhowmick and Debashish Goswami and Soumalya Joardar},
  journal={arXiv: Quantum Algebra},
  year={2016}
}

J. Bhowmick, Debashish Goswami, Soumalya Joardar

Published 2016

Mathematics

arXiv: Quantum Algebra

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We prove the existence and uniqueness of Levi-Civita connections for a noncommutative pseudo-Riemannian metric on a class of centered bimodule of one forms. As an application, we compute the Ricci and scalar curvature for a general conformal perturbation of the canonical metric on the noncommutative $2$-torus as well as for a natural metric on the quantum Heisenberg manifold. For the latter, the scalar curvature turns out to be a negative constant.