A generalized Stiefel manifold is the of orthonormal frames in a vector space with nondegenerated bilinear or hermitian form. In this article, Isometry group manifolds are computed at least up to connected components an explicit This done by considering natural nonassociative algebra m associated affine structure manifold, computing explicitly automorphism Aut(

We study left-invariant generalized K\"ahler structures on almost abelian Lie groups, i.e., solvable groups with a codimension-one normal subgroup. In particular, we classify six-dimensional which admit complex structure and establish of those have Hermitian whose fundamental 2-form is $\partial \bar \partial$-closed. obtain classification determine the 6-dimensional compact solvmanifolds admit...