Integrable Top Equations associated with Projective Geometry over Z_2

TL;DR

This paper introduces a family of integrable top equations linked to projective geometry over Z_2, generalizing the 3D Euler top, with solutions expressed via Riemann surface integrations.

Contribution

It presents a novel class of integrable top equations associated with Z_2 projective geometry, extending the Euler top to higher dimensions.

Findings

Derived (2^n-1)D top equations with integrability properties.

Provided explicit solutions involving Riemann surface integrations.

Generalized classical Euler top equations to higher-dimensional settings.

Abstract

We give a series of integrable top equations associated with the projective geometry over Z_2 as a (2^n-1)-dimensional generalisation of the 3D Euler top equations. The general solution of the (2^n-1)D top is shown to be given by an integration over a Riemann surface with genus (2^{n-1}-1)^2.