An intrinsic characterization of fibre bundles associated with homogeneous spaces defined by Lie group automorphisms

Abstract

Let G be a connected Lie group, 27 a group acting on G by automorphisnl~ and H an open subgroup of the fixed point set G z" of 27. The homogeneous spaces G/H have been studied extensively by WOLF and GRAY [6] in case 27 is cyclic. The case where Z is of order two axe just the symmetric spaces. Now let F be a manifold on which H acts on the left, and consider the fibre bundle M = G • F with typical fibre F, H associated with the principal fibre bundle G over G/H with structure group H. For a, b e G, x, y e F and a e 27 set