Noncompactness Property of Fibers and Singularities of Non-Euclidean Kovalevskaya System on Pencil of Lie Algebras

It is shown that Liouville foliations of the family of non-Euclidean analogs of Kovalevskaya integrable system on a pencil of Lie algebras have both compact and noncompact fibers. There exists a bifurcation of their compact common level surface into a noncompact one that has a noncompact singular fiber. In particular, this is true for the non-Euclidean $$e(2,1)$$ -analog of the Kovalevskaya case of rigid body dynamics. In the case of nonzero area integral, an effective criterion for existence of a noncompact connected component of the common level surface of first integrals and Casimir functions is proved.