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Some properties of symplectic and hyper-Kählerian structures. (English. Russian original) Zbl 0842.53019
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 511-514 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 3, 304-306 (1994).
It is well known, that the Poincaré series for the moduli space of solutions of the gravitational field equations in empty space is a rational function, because its coefficients are polynomials. The author shows that a similar result holds for Kähler and hyper-Kählerian structures. The technique used by the author is as follows. Given the natural action of the group of germs of diffeomorphisms at a point on the space of jets of a geometric object (for instance, the Kähler form), the dimension of the foliation determined by the orbits is computed.
MSC:
53B35 Local differential geometry of Hermitian and Kählerian structures
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
32Q15 Kähler manifolds
53C12 Foliations (differential geometric aspects)
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