Abstract:
We introduce a complete invariant for Weyl manifolds, called a Poincaré–Cartan class. Applying the constructions of the Weyl manifold to complex manifolds via the Poincaré–Cartan class, we propose the notion of a noncommutative Kähler manifold. For a given Kähler manifold, the necessary and sufficient condition for a Weyl manifold to be a noncommutative Kähler manifold is given. In particular, there exists a noncommutative Kähler manifold for any Kähler manifold. We also construct the noncommutative version of the S 1-principal bundle over a quantizable Weyl manifold.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 4 April 1997 / Accepted: 12 October 1997
Rights and permissions
About this article
Cite this article
Omori, H., Maeda, Y., Miyazaki, N. et al. Poincaré–Cartan Class and Deformation Quantization of Kähler Manifolds . Comm Math Phys 194, 207–230 (1998). https://doi.org/10.1007/s002200050356
Issue Date:
DOI: https://doi.org/10.1007/s002200050356