arXiv math/05014132005-01-24math.DS

Integrability versus topology of configuration manifolds and domains of possible motions

M. Rudnev, V. Ten

英文摘要：

We establish a generic sufficient condition for a compact $n$-dimensional manifold bearing an integrable geodesic flow to be the $n$-torus. As a complementary result, we show that in the case of domains of possible motions with boundary, the first Betti number of the domain of possible motions may be arbitrarily large.

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