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.
Killing tensors as irreducible representations of the general linear group
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Proves Liouville integrability of the magnetic geodesic flow on S^n with constant 2-form via quadratic and linear integrals in momenta.
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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.