Invariant classification of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space

TL;DR

This paper provides an invariant classification of rotationally symmetric R-separable webs for the Laplace equation in Euclidean space using invariants of an associated real binary quartic, advancing the understanding of separability structures.

Contribution

It introduces a new invariant characterization of these webs based on invariants and covariants of a real binary quartic linked to the characteristic conformal Killing tensor.

Findings

Invariant classification scheme for R-separable webs

Connection between webs and real binary quartic invariants

Enhanced understanding of separability in Euclidean space

Abstract

An invariant characterization of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space is given in terms of invariants and covariants of a real binary quartic canonically associated to the characteristic conformal Killing tensor which defines the webs.