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On biharmonic functions on vector bundles

Mohamed Tahar Kadaoui Abbassi, Souhail Doua, Ibrahim Lakrini

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.

On biharmonic functions 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 -radial functions on vector bundle manifolds and, as a consequence, we will construct an infinite two-parameter family of proper biharmonic functions.
Paper Structure (6 sections, 50 equations)

This paper contains 6 sections, 50 equations.

Table of Contents

  1. Preliminaries
  2. Harmonic and biharmonic functions
  3. Vector bundles and spherically symmetric metrics
  4. Some classes of functions on vector bundles
  5. Biharmonicity of vertical lifts of functions to vector bundles
  6. Biharmonicity of r-radial functions

Theorems & Definitions (6)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof