#### Vol. 11, No. 5, 2018

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Quasipositive curvature on a biquotient of Sp$(3)$

### Jason DeVito and Wesley Martin

Vol. 11 (2018), No. 5, 787–801
##### Abstract

Suppose ${\varphi }_{3}:Sp\left(1\right)\to Sp\left(2\right)$ denotes the unique irreducible complex $4$-dimensional representation of $Sp\left(1\right)=SU\left(2\right)$, and consider the two subgroups ${H}_{i}\subseteq Sp\left(3\right)$ with ${H}_{1}=\left\{diag\left({\varphi }_{3}\left({q}_{1}\right),{q}_{1}\right):{q}_{1}\in Sp\left(1\right)\right\}$ and ${H}_{2}=\left\{diag\left({\varphi }_{3}\left({q}_{2}\right),1\right):{q}_{2}\in Sp\left(1\right)\right\}$. We show that the biquotient ${H}_{1}\setminus Sp\left(3\right)∕{H}_{2}$ admits a quasipositively curved Riemannian metric.

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##### Keywords
biquotients, homogeneous spaces, quasipositive sectional curvature
##### Mathematical Subject Classification 2010
Primary: 53C20, 57S25
Secondary: 53C30