Projective homogeneity
The author is occupied with the followng problem: Given a manifold M with a projective structure P, which are the necessary and sufficient conditions for (M,P) to be a reductive homogeneous space with respect to a connected Lie group of transformations of M preserving the projective structure P ? In fact, the autor gives a deeper insight into the structure of a projective homogeneous space (the necessity part). The sufficient conditions contain additional assumptions about the projective manifold (M,P), and they require the existence of a complete connection satisfying certain properties (which enables to use a classical result by Kostant). Thus the problem to find geometrically natural sufficient conditions remains still open. For the affine case, such natural characterization of reductive homogeneous spaces is given in the reviewer's book Generalized symmetric spaces [Lect. Notes Math. 805 (1980; Zbl 0431.53042), theorem I.25]. Here everything is reduced to the simple holonomy properties of the given affine connection.
scientific article; zbMATH DE number 4120948