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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
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