A maximally superintegrable system on an n-dimensional space of nonconstant curvature

TL;DR

This paper introduces a new maximally superintegrable Hamiltonian system in n-dimensional space with nonconstant curvature, providing explicit integrals and solutions, advancing understanding of integrability in curved spaces.

Contribution

It presents the first example of a maximally superintegrable system on an n-dimensional nonconstant curvature space, including explicit integrals and solutions.

Findings

System admits 2n-1 quadratic first integrals

Provides three complete sets of integrals in involution

Solves equations of motion explicitly

Abstract

A novel Hamiltonian system in n dimensions which admits the maximal number 2n-1 of functionally independent, quadratic first integrals is presented. This system turns out to be the first example of a maximally superintegrable Hamiltonian on an n-dimensional Riemannian space of nonconstant curvature, and it can be interpreted as the intrinsic Smorodinsky-Winternitz system on such a space. Moreover, we provide three different complete sets of integrals in involution and solve the equations of motion in closed form.