## Projective nilmanifolds. (Nilvariétés projectives.)(French)Zbl 0839.53033

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)

### MSC:

 53C30 Differential geometry of homogeneous manifolds 22E25 Nilpotent and solvable Lie groups

### Keywords:

affine structure; nilmanifold; projective structure
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