Proves Kiyohara's 2001 metrics with arbitrary high-degree polynomial integrals are not superintegrable, solving two Bolsinov-Kozlov-Fomenko conjectures via a new theorem on Poisson brackets of integrals.
The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta
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Killing tensors on products of Riemannian manifolds with one compact factor are reducible sums of factor tensors.
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Real-analyticity of 2-dimensional superintegrable metrics and solution of two Bolsinov-Kozlov-Fomenko conjectures
Proves Kiyohara's 2001 metrics with arbitrary high-degree polynomial integrals are not superintegrable, solving two Bolsinov-Kozlov-Fomenko conjectures via a new theorem on Poisson brackets of integrals.
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Killing tensors on reducible spaces
Killing tensors on products of Riemannian manifolds with one compact factor are reducible sums of factor tensors.