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Conformal symplectic geometry, deformations, rigidity and geometrical (KMS) conditions. (English) Zbl 0589.53037

From the authors’ introduction: ”In Part I, we define and study the notion of the \(*^ f\)-product in a general context and show how the conformal Poisson geometry or symplectic geometry necessarily appears. In Part II, we study the deformations of a \(*^ f\)-product on a symplectic manifold and prove a rigidity theorem in the framework of \(*^ f\)- products (f fixed). We can, however, deform a star product in suitable \(*^ f\)-products, but then we have no equivalence property. We translate this result in terms of statistical mechanics and thus obtain a correct generalization of our results in C. R. Acad. Sci., Paris, Sér. I 293, 347-350 (1981; Zbl 0482.58037).”
Reviewer: A.Verona

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58H15 Deformations of general structures on manifolds
53D50 Geometric quantization

Citations:

Zbl 0482.58037
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References:

[1] BasartH., FlatoM., LichnerowiczA., and ?ternheimer, D., C.R. Acad. Sci. Paris 298 I, 405 (1984); Lett. Math. Phys. 8 483-494 (1984).
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[3] BasartH. and LichnerowiczA., C.R. Acad. Sci. Paris 293 I, 347 (1981).
[4] Rubio, R., C.R. Acad. Sci. Paris 299 I (1984).
[5] Notations of [1].
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[8] DeWildeM. and LecomteP., Lett. Math. Phys. 7, 487 (1983). · Zbl 0526.58023 · doi:10.1007/BF00402248
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