Poincaré-Cartan class and deformation quantization of Kähler manifolds

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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 S1-principal bundle over a quantizable Weyl manifold.

Original languageEnglish
Pages (from-to)207-230
Number of pages24
JournalCommunications in Mathematical Physics
Issue number1
Publication statusPublished - 1998 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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