an:00804003
Zbl 0842.53019
Shmelev, A. S.
Some properties of symplectic and hyper-K??hlerian structures
EN
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).
00027864
1994
j
53B35 53C15 32Q15 53C12
K??hler structures; hyper-K??hler structures; moduli space of metrics
It is well known, that the Poincar?? 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 K??hler and hyper-K??hlerian 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 K??hler form), the dimension of the foliation determined by the orbits is computed.
M.de Le??n (Madrid)