Quasipositive curvature on a biquotient of Sp(3)

DeVito, Jason; Martin, Wesley

doi:10.2140/involve.2018.11.787

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

Jason DeVito and Wesley Martin

Vol. 11 (2018), No. 5, 787–801

DOI: 10.2140/involve.2018.11.787

Abstract

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

Keywords

biquotients, homogeneous spaces, quasipositive sectional curvature

Mathematical Subject Classification 2010

Primary: 53C20, 57S25

Secondary: 53C30

Milestones

Received: 29 September 2016

Revised: 26 August 2017

Accepted: 20 November 2017

Published: 2 April 2018

Communicated by Kenneth S. Berenhaut

Authors

Jason DeVito
Department of Mathematics and Statistics University of Tennessee Martin Martin, TN 38238 United States

Wesley Martin
Department of Education University of Tennessee Martin Martin, TN 38238 United States

Vol. 11, No. 5, 2018