Modular Gaussian curvature

  • Matthias Lesch
  • Henri MoscoviciEmail author


This is a brief survey of the main developments that led to the emergence of the quantized analogue of Gaussian curvature for the noncommutative torus and to its current understanding. It highlights the role of Connes’ pseudodifferential calculus as the crucial technical tool for the explicit computation of the modular Gaussian curvature, the effectiveness of the variational methods, and it sheds more light on the intrinsic geometric meaning of the Morita equivalence in this context.



The work of M.L. was partially supported by the Hausdorff Center for Mathematics, Bonn, and the work of H. M. was partially supported by the National Science Foundation award DMS-1600541.


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Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BonnBonnGermany
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA

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