A Fedosov star product of the Wick type for Kähler manifolds. (English) Zbl 0892.53028

Bordemann, M.; Waldmann, S.

Lett. Math. Phys. 41, No. 3, 243-253 (1997).

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”.

Reviewer: E.García-Río (Santiago de Compostela)

MSC:

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

Keywords:

star product of Wick type; Fedosov star product of Weyl type; Kähler manifold