Corpus ID: 55226642

A new look at Levi-Civita connection in noncommutative geometry

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