Benoist, Yves Projective nilmanifolds. (Nilvariétés projectives.) (French) Zbl 0839.53033 Comment. Math. Helv. 69, No. 3, 447-473 (1994). A nilmanifold is a compact quotient of a nilpotent Lie group by a discrete subgroup. An affine (resp. projective) structure on a \(C^\infty\)-manifold is an atlas whose charts take values in \(\mathbb{R}^n\) (resp. \(\mathbb{S}^n\)) and whose coordinate changes are affine (resp. projective) transformations. The author studies properties of affine and projective structures on nilmanifolds. The main results are: 1) On “filiform” nilmanifolds, any affine or projective structure is left invariant. 2) There exist nilmanifolds without projective structure. Reviewer: G.Roos (Poitiers) Cited in 1 ReviewCited in 11 Documents MSC: 53C30 Differential geometry of homogeneous manifolds 22E25 Nilpotent and solvable Lie groups Keywords:affine structure; nilmanifold; projective structure PDFBibTeX XMLCite \textit{Y. Benoist}, Comment. Math. Helv. 69, No. 3, 447--473 (1994; Zbl 0839.53033) Full Text: DOI EuDML