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

TL;DR

This paper classifies the topological structure of energy surfaces in a specific integrable Hamiltonian system on the Lie algebra so(4), using Fomenko-Zieschang invariants to understand their diffeomorphism classes.

Contribution

It determines the diffeomorphism classes of energy level surfaces for the Kovalevskaya integrable case on so(4), extending previous invariants analysis.

Findings

Classified the diffeomorphism types of energy surfaces

Applied Fomenko-Zieschang invariants to this integrable system

Provided a topological description of the energy level sets

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 $\textrm{so}(4)$. We start from Fomenko-Zieschang invariants of Lioville foliations on these manifolds that were calculated by the author earlier.