Poincaré-Cartan class and deformation quantization of Kähler manifolds

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

研究成果: Article

9 引用 (Scopus)

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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.

元の言語English
ページ(範囲)207-230
ページ数24
ジャーナルCommunications in Mathematical Physics
194
発行部数1
DOI
出版物ステータスPublished - 1998 1 1
外部発表Yes

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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