# Closed ray nil-affine manifolds and parabolic geometries

@inproceedings{Alexandre2021ClosedRN, title={Closed ray nil-affine manifolds and parabolic geometries}, author={Raphael Alexandre}, year={2021} }

Ray nil-affine geometries are defined on nilpotent spaces. They occur in every parabolic geometry and in those cases, the nilpotent space is an open dense subset of the corresponding flag manifold. We are interested in closed manifolds having a ray nil-affine structure. We show that under a rank one condition on the isotropy, closed manifolds are either complete or their developing map is a cover onto the complement of a nilaffine subspace. We prove that if additionally there is a parallel…

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