### 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.

Original language | English |
---|---|

Pages (from-to) | 207-230 |

Number of pages | 24 |

Journal | Communications in Mathematical Physics |

Volume | 194 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Poincaré-Cartan class and deformation quantization of Kähler manifolds'. Together they form a unique fingerprint.

## Cite this

Omori, H., Maeda, Y., Miyazaki, N., & Yoshioka, A. (1998). Poincaré-Cartan class and deformation quantization of Kähler manifolds.

*Communications in Mathematical Physics*,*194*(1), 207-230. https://doi.org/10.1007/s002200050356