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Integrability versus topology of configuration manifolds and domains of possible motions

M. Rudnev·V. Ten
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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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M. Rudnev, V. Ten. 2005-01-24. Integrability versus topology of configuration manifolds and domains of possible motions. https://arxiv.org/abs/math/0501413

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