New homogeneous Einstein metrics on quaternionic Stiefel manifolds

Andreas Arvanitoyeorgos, Yusuke Sakane, Marina Statha

Published 2018-10-01Version 1

We consider invariant Einstein metrics on the quaternionic Stiefel manifolds $V_p\bb{H} ^n$ of all orthonormal $p$-frames in $\bb{H}^n$. 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 $V_{p}\bb{H}^{n} \cong \Sp(n)/\Sp(n-p)$, where $n = k_1 + k_2 + k_3$ and $p = n-k_3$. We view $V_{p}\bb{H}^{n}$ as a total space over the genaralized Wallach space $\Sp(n)/(\Sp(k_1)\times\Sp(k_2)\times\Sp(k_3))$ and over the generalized flag manifold $\Sp(n)/(\U(p)\times\Sp(n-p))$.