Projective homogeneity
type: Item
instance of: scholarly article
title: Projective homogeneity
zbMATH Open document ID: 0684.53041
DOI: 10.1007/BF01160116
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155402
review text: 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.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53B10
Mathematics Subject Classification ID: 53A20
zbMATH DE Number: 4120948
zbMATH Keywords: reductive homogeneous space
zbMATH Keywords: projective structure
zbMATH Keywords: complete connection
author: Fabio Podestà
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
Wikidata QID: Q125274042
cites work: Invariant flat projective structures on homogeneous spaces
cites work: Q5658761
cites work: Q5565587
cites work: A Characterization of Invariant Affine Connections
cites work: Some theorems on projective hyperbolicity
OpenAlex ID: W4241164042
description: scientific article; zbMATH DE number 4120948