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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.
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)