New homogeneous Einstein metrics on quaternionic Stiefel manifolds

2018/10/01 by Andreas Arvanitoyeorgos, Yusuke Sakane, Marina Statha · 1 citation
Mathematics · #math.DG #msc:53C25 #msc:53C30 #msc:13P10 #msc:65H10 #msc:68W30

paper · pdf · doi:10.1515/advgeom-2018-0014

published as Adv. Geom. 18 (4) (2018) 509-524 · 19 pages

arxiv created 2018/10/01 · arxiv updated 2018/11/01

Abstract

We consider invariant Einstein metrics on the quaternionic Stiefel manifolds V_pℍ ⁿ of all orthonormal p-frames in ℍⁿ. This manifold is diffeomorphic to the homogeneous space Sp(n) / Sp(n-p) and its isotropy representation contains equivalent summands. We obtain new Einstein metrics on V_pℍⁿ ≅ Sp(n)/Sp(n-p), where n = k₁ + k₂ + k₃ and p = n-k₃. We view V_pℍⁿ as a total space over the generalized Wallach space Sp(n) / (Sp(k₁) × Sp(k₂) × Sp(k₃)) and over the generalized flag manifold Sp(n) / (U(p) × Sp(n-p)).

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• Homogeneous Einstein metrics on Stiefel manifolds associated to flag manifolds with two isotropy summands