On biharmonic functions on vector bundles

TL;DR

This paper investigates harmonic and biharmonic functions on vector bundles with spherically symmetric metrics, constructing an infinite family of proper biharmonic functions through analysis of vertical lifts and radial functions.

Contribution

It introduces new methods for constructing proper biharmonic functions on vector bundles, expanding the understanding of biharmonicity in geometric analysis.

Findings

Constructed an infinite two-parameter family of proper biharmonic functions.

Analyzed biharmonicity of vertical lifts and r-radial functions.

Provided insights into harmonic analysis on vector bundles.

Abstract

This paper is devoted to the investigation of harmonic and biharmonic functions on vector bundles equipped with spherically symmetric metrics. We will study the biharmonicity of vertical lifts of functions as well as $r$-radial functions on vector bundle manifolds and, as a consequence, we will construct an infinite two-parameter family of proper biharmonic functions.