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A Fedosov star product of the Wick type for Kähler manifolds. (English) Zbl 0892.53028
Author’s abstract: “In this letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differenciation. Moreover, we define the notion of a star product of the Wick type on every Kähler manifold by a straightforward generalization of the corresponding star product in \(\mathbb{C}^n\): the corresponding sequence of bidifferential operators differentiates its first argument in holomorphic directions and its second argument in antiholomorphic directions. By a Fedosov type procedure, we give an existence proof of such star products for any Kähler manifold”.

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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