Poincaré-Cartan class and deformation quantization of Kähler manifolds

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 S1-principal bundle over a quantizable Weyl manifold.

Original languageEnglish
Pages (from-to)207-230
Number of pages24
JournalCommunications in Mathematical Physics
Volume194
Issue number1
Publication statusPublished - 1998
Externally publishedYes

Fingerprint

Deformation Quantization
Class
Principal Bundle
Complex Manifolds
bundles
Necessary Conditions
Invariant

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Poincaré-Cartan class and deformation quantization of Kähler manifolds. / Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira.

In: Communications in Mathematical Physics, Vol. 194, No. 1, 1998, p. 207-230.

Research output: Contribution to journalArticle

Omori, Hideki ; Maeda, Yoshiaki ; Miyazaki, Naoya ; Yoshioka, Akira. / Poincaré-Cartan class and deformation quantization of Kähler manifolds. In: Communications in Mathematical Physics. 1998 ; Vol. 194, No. 1. pp. 207-230.
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