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

Suppose ϕ3 : Sp(1) Sp(2) denotes the unique irreducible complex 4-dimensional representation of Sp(1) = SU(2), and consider the two subgroups Hi Sp(3) with H1 = {diag(ϕ3(q1),q1) : q1 Sp(1)} and H2 = {diag(ϕ3(q2),1) : q2 Sp(1)}. We show that the biquotient H1Sp(3)H2 admits a quasipositively curved Riemannian metric.

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biquotients, homogeneous spaces, quasipositive sectional curvature
Mathematical Subject Classification 2010
Primary: 53C20, 57S25
Secondary: 53C30
Received: 29 September 2016
Revised: 26 August 2017
Accepted: 20 November 2017
Published: 2 April 2018

Communicated by Kenneth S. Berenhaut
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