• Corpus ID: 244345904

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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References

SHOWING 1-10 OF 29 REFERENCES

Closed ray affine manifolds

We consider closed manifolds that possess a so called rank one ray structure. That is a (flat) affine structure such that the linear part is given by the products of a diagonal transformation and a

Geodesic convexity and closed nilpotent similarity manifolds

Some nilpotent Lie groups possess a transformation group analogous to the similarity group acting on the Euclidean space. We call such a pair a nilpotent similarity structure. It is notably the case

Proper quasi-homogeneous domains in flag manifolds and geometric structures

In this paper we study domains in flag manifolds which are bounded in an affine chart and whose projective automorphism group acts co-compactly. In contrast to the many examples in real projective

The radiance obstruction and parallel forms on affine manifolds

A manifold M is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine. When they are locally linear M is called radiant. The obstruction to radiance is a

On the Conformal and CR Automorphism Groups

This paper concerns the behavior of conformal diffeomorphisms between Riemannian manifolds, and that of CR diffeomorphisms between strictly pseudoconvex CR manifolds, We develop a new approach to the

On the transformation group of a real hypersurface

The group of biholomorphic transformations leaving fixed a strongly pseudoconvex real hypersurface in a complex manifold is a Lie group. In this paper it is shown that the Chern-Moser invariants must

Convex cocompactness in pseudo-Riemannian hyperbolic spaces

Anosov representations of word hyperbolic groups into higher-rank semisimple Lie groups are representations with finite kernel and discrete image that have strong analogies with convex cocompact

Dynamics on flag manifolds: domains of proper discontinuity and cocompactness

For noncompact semisimple Lie groups G with finite center, we study the dynamics of the actions of their discrete subgroups Gamma < G on the associated partial flag manifolds G / P. Our study is

Autour de la conjecture de L. Markus sur les variétés affines

SummaryFor any subgroupG of (ℝn), we introduce some integer discG≦n called thediscompacity ofG. This number measures to what extent the closure ofG is not compact. The Markus' conjecture says that a

The conjectures on conformal transformations of Riemannian manifolds

Let (M, g) be a Riemannian /t-manifold with Riemannian metric g. Throughout this paper manifolds under consideration are always assumed to be connected and smooth. For a smooth function p on M, a