Quasi-positive curvature on a biquotient of $Sp(3)$

Abstract

Suppose ${\varphi }_3:Sp(1)\to Sp(2)$ denotes the unique irreducible $4$-dimensional representation of $Sp(1)=SU(2)$ and consider the two subgroups $H_1,H_2\subseteq Sp(3)$ with $H_1=\{\mathrm{diag}({\varphi }_3(q_1),q_1):q_1\in Sp(1)\}$ and $H_2=\{\mathrm{diag}({\varphi }_3(q_2),1):q_2\in Sp(1)\}$. We show that the biquotient $H_1\backslash Sp(3)/H_2$ admits a quasi-positively curved Riemannian metric.

References in corpus (1)

• The classification and curvature of biquotients of the form $Sp(3)//Sp(1{)}^2$