Geodesic
Noncompactness property of fibers and singularities of non-Euclidean Kovalevskaya system on pencil of Lie algebras
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2020), pp. 56-59

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It is shown that Liouville foliations of the family on non-Euclidean analogs of Kovalevskaya integrable system on a pencil of Lie algebras have both compact and noncompact fibers. A bifurcation of their compact common level surface into a noncompact one exists and has a noncompact singular fiber. In particular, this is true for the non-Euclidean $e(2, 1)$-analogue of the Kovalevskaya case of rigid body dynamics. For the case of nonzero area integral, we prove an effective criterion of existence of a noncompact component of the common level surface of first integrals and Casimir functions. 
@article{VMUMM_2020_6_a8,
     author = {V. A. Kibkalo},
     title = {Noncompactness property of fibers and singularities of {non-Euclidean} {Kovalevskaya} system on pencil of {Lie} algebras},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {56--59},
     publisher = {mathdoc},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_6_a8/}
}
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V. A. Kibkalo. Noncompactness property of fibers and singularities of non-Euclidean Kovalevskaya system on pencil of Lie algebras. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2020), pp. 56-59. http://geodesic.mathdoc.fr/item/VMUMM_2020_6_a8/