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”.


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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