### 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 |

Publication status | Published - 1998 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*194*(1), 207-230.

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 194, no. 1, pp. 207-230.

}

TY - JOUR

T1 - Poincaré-Cartan class and deformation quantization of Kähler manifolds

AU - Omori, Hideki

AU - Maeda, Yoshiaki

AU - Miyazaki, Naoya

AU - Yoshioka, Akira

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032474122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032474122&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032474122

VL - 194

SP - 207

EP - 230

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -