Topology of isoenergy surfaces of Kovalevskaya integrable case on the Lie algebra so(4)

Abstract

In the paper we determine the class of diffeomorphism of three-dimensional regular common level surfaces of Hamiltonian and Casimir functions for the analog of Kovalevskaya case on Lie algebra $\text{so}(4)$. We start from Fomenko-Zieschang invariants of Lioville foliations on these manifolds that were calculated by the author earlier.