A two-component geodesic equation on a space of constant positive curvature

TL;DR

This paper introduces a novel two-component geodesic equation on a space with constant positive curvature, generalizing the two-component Hunter-Saxton equation in one dimension, and explores its geometric properties.

Contribution

It presents a new two-component geodesic equation on a positively curved space, extending the Hunter-Saxton equation to higher dimensions with constant curvature.

Findings

The equation reduces to the Hunter-Saxton equation in one dimension.

The underlying space has constant positive curvature.

The geometric structure of the equation is characterized.

Abstract

We propose a new two-component geodesic equation with the unusual property that the underlying space has constant positive curvature. In the special case of one space dimension, the equation reduces to the two-component Hunter-Saxton equation.