ISOMETRY GROUPS OF GENERALIZED STIEFEL MANIFOLDS

Abstract

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