Biharmonic functions on the special unitary group SU(2)

TL;DR

This paper constructs new proper biharmonic functions on the special unitary group SU(2) and hyperbolic space H^3, expanding the understanding of biharmonic functions on these geometric structures.

Contribution

It introduces novel proper biharmonic functions on SU(2) and H^3 using a duality principle, advancing the theory of biharmonic functions on Lie groups and symmetric spaces.

Findings

New proper biharmonic functions on SU(2)

Proper biharmonic functions on H^3 derived via duality

Enhanced methods for constructing biharmonic functions

Abstract

We construct new proper biharmonic functions defined on open and dense subsets of the special unitary group SU(2). Then we employ a duality principle to obtain new proper biharmonic functions from the non-compact 3-dimensional hyperbolic space H^3.