Liouville Type Theorem about $p$-harmonic 1 form, $p$-harmonic map and harmonic $ q $ form

TL;DR

This paper establishes Liouville theorems for p-harmonic functions, 1-forms, and harmonic q-forms on Riemannian manifolds using normalized integral Ricci and BiRic curvatures, extending classical results.

Contribution

It introduces new Liouville theorems for p-harmonic forms and functions based on BiRic curvature, broadening the scope of geometric analysis in Riemannian geometry.

Findings

Liouville theorem for p-harmonic functions using normalized integral Ricci curvature

Liouville theorem for p-harmonic 1-forms using BiRic curvature

Liouville theorem for harmonic q-forms (q≥2) using BiRic curvature

Abstract

In this paper, we will use the normalized intetral Ricci curvature to investigate Liouville type property of $ p $ harmonic function on Riemannian manifold. secondly, we will use the BiRic curvature to obtian Liuville theorem for $ p $ harmonic function or $ p $ harmonic 1 form. Lastly, we we will use the BiRic curvature to obtian Liouville theorem forharmonic $ q(q\geq 2)$ form.