New constructions of biharmonic polynomial maps between spheres

TL;DR

This paper introduces new methods for constructing proper biharmonic maps between spheres using harmonic polynomial maps, expanding the toolkit for geometric analysis of such maps.

Contribution

It provides a novel approach to generate proper biharmonic maps between spheres based on harmonic homogeneous polynomial maps of different degrees.

Findings

Derived explicit formulas for the bitension field of diagonal maps between spheres.

Developed a method to generate proper biharmonic maps from harmonic polynomial maps.

Established a construction technique for proper biharmonic product maps.

Abstract

In this paper, we study diagonal maps between spheres given by two homogeneous polynomial maps between spheres, defined on the same domain sphere. First we find their bitension field, then we give a method for generating proper biharmonic maps between spheres, relying on harmonic homogeneous polynomial maps of different degrees. Further, we establish a result for constructing proper biharmonic product maps using harmonic homogeneous polynomial maps between spheres.