New homogeneous Einstein metrics on quaternionic Stiefel manifolds

Abstract

Abstract We consider invariant Einstein metrics on the quaternionic Stiefel manifold V p ℍ n of all orthonormal p -frames in 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 ℍ n ≅ Sp( n )/Sp( n − p ), where n = k 1 + k 2 + k 3 and p = n − k 3 . We view V p ℍ n as a total space over the generalized Wallach space Sp( n )/(Sp( k 1 )×Sp( k 2 )×Sp( k 3 )) and over the generalized flag manifold Sp( n )/(U( p )×Sp( n − p )).