Conformal vector fields on vector bundle manifolds with spherically symmetric metrics

Abstract

In this paper, we investigate conformal vector fields on vector bundle manifolds when endowed with spherically symmetric metrics. We construct a class of non-trivial conformal vector fields, and establish a classification theorem for conformal horizontal vector fields. Conformal gradient vector fields are investigated and closed vector fields are studied in detail. Finally, we focus on finding some examples of parallel vector fields as well as some of their classification results.

On biharmonic functions on vector bundles

“…Spherically symmetric metrics have been extensively studied in [12,9,8,10,11]. We shall recall some necessary technical tools we will be using in the forthcoming calculations.…”