Steady gradient Ricci Yang-Mills solitons on 2-orbifolds

Abstract

Following the recent work of M. Womack \cite{Wo26} we consider the steady Ricci Yang-Mills solitons on 2d surfaces containing orbifold point ${\mathbb{R}}^2/{\mathbb{Z}}_p$. We show that there are a family of solitons depending parameter $\lambda$ which approaches to ${\mathbb{Z}}_p$-quotient of Hamilton cigar soliton as $\lambda \to (-2/p{)}^{+}$ and approaches to (after rescaling) ${\mathbb{Z}}_p$-quotient of round sphere as $\lambda \to \infty$. For any integer $q>p$ there is a $\lambda$ whose corresponding soliton metric is defined on football orbifold $S_{p,q}^2$.

10 pages