Einstein Metrics on the Symplectic Group Which Are Not Naturally Reductive

On Left-Invariant Einstein Riemannian Metrics That Are Not Geodesic Orbit

“…Hence we get Theorem 2. A Riemannian homogeneous manifold (M, g) is a geodesic orbit manifold if and only if for any X ∈ m there are V ∈ h and U ∈ h (see (5)) such that for any Y ∈ m the equality…”

“…In [11] Z. Chen and K. Liang found three naturally reductive and one non naturally reductive Einstein metric on the compact Lie group F 4 . Also, in [5], the authors obtained new leftinvariant Einstein metrics on the symplectic group Sp(n) (n ≥ 3), and in [12] I. Chrysikos and Y. Sakane obtained new non naturally reductive Einstein metrics on exceptional Lie groups. In the recent paper [6], the authors obtained new left-invariant Einstein metrics on the compact Lie groups SO(n) (n ≥ 7) which are not naturally reductive.…”

New Einstein metrics on the Lie group $\mathrm{SO}(n)$ which are not naturally reductive

“…In [ChLi] Z. Chen and K. Liang found three naturally reductive and one non naturally reductive Einstein metric on the compact Lie group F 4 . Also, in [ArSaSt2] the authors obtained new left-invariant Einstein metrics on the symplectic group Sp(n) (n ≥ 3), and in [ChSa] I. Chrysikos and the second author obtained non naturally reductive Einstein metrics on exceptional Lie groups. We also mention the works [GiLuPo], [Po] by G.W.…”

New homogeneous Einstein metrics on quaternionic Stiefel manifolds

“…The first invariant Einstein metrics on the quaternionic Stiefel manifolds V p H n = Sp(n)/ Sp(n − p) were obtained by G. Jensen in [Je], by using Riemannian submersions. Invariant Einstein metrics on the two marginal cases V 1 H n = S 4n−1 and V n H n = Sp(n) have been studied in [Zi] and [ArSaSt2] respectively.…”