ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 58F17, 53C22, 15A72 Topalov, Petar, Inst. of Mathematics, BAS, Bulgaria A family of 3-integrable metrics A Riemannian metric is called 3-integrable if its geodesic flow admits a first integral which is polinomial of third degree in momenta and which is independent from the energy integral. There is known only few examples of 3-integrable metrics. We obtain a big new family of 3-integrable metrics. Explicit formulae are obtained. The family contains three classical cases of 3-integrable metrics — Toda lattice, Holt potential and Goryachev-Chaplygin top. Part of these results is joint work with V. Matveev and H. Dullin.