Nonexistence of weakly stable Yang-Mills fields

TL;DR

This paper proves the nonexistence of nontrivial weakly stable Yang-Mills connections near the standard metric on high-dimensional spheres and explores their stability on warped product manifolds.

Contribution

It establishes a local nonexistence result for weakly stable Yang-Mills fields on spheres and investigates stability properties on warped product manifolds.

Findings

No nontrivial weakly stable Yang-Mills connections near the standard metric on $S^n$ for $n extgreater=5$

Stability analysis of Yang-Mills connections on warped product manifolds

Neighborhood in $C^2$ topology where such connections do not exist

Abstract

In this paper we prove that there is a neighborhood in the $C^2$ topology of the usual metric on the Euclidean sphere $S^n (n\geq 5)$ such that there is no nontrivial weakly stable Yang-Mills connections for any metric $\tilde{g}$ in this neighborhood. We also study the stability of Yang-Mills connections on the warped product manifolds.