Integrability versus topology of configuration manifolds and domains of possible motions
M. Rudnev, V. Ten
Abstract
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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