Some classes of harmonic functions on vector bundles

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.…”

“…In the general context of vector bundles the first and third authors studied, in [11], the harmonicity of the following classes of functions:…”

“…Using induced local frames of the form (7) and Lemma 2.1, in [11], the authors proved the following formulas:…”

“…In the context of geometry of vector bundles, the first and third authors studied harmonic function theory for a class of Riemannian metrics known as spherically symmetric metrics (cf. [11]). They also used this to infer interesting results on the geometry of these spaces.…”

“…They also used this to infer interesting results on the geometry of these spaces. In particular, they studied the harmonicity of vertical lifts as well as a class of functions known as r-radial functions [11]. We will investigate, in this paper, the biharmonicity of these classes and we will explicitly construct an infinite two-parameter family of examples of proper biharmonic functions on vector bundle manifolds endowed with spherically symmetric metrics.…”