Closed similarity lorentzian affine manifolds
Abstract
A Sim(n-1,1) affine manifold is an affine manifold whose linear holonomy is contained in the similarity lorentzian group but not in the lorentzian group. The class of similarity lorentzian affine manifolds is a small part in the nice class of conformally lorentzian flat manifolds. In this paper we show that a compact Sim(n-1,1) affine manifold is incomplete. We characterize the universal cover of radiant compact Sim(n-1,1) affine manifolds whose developing map is injective. Let q be the quadratic form which define the Sim(n-1,1) structure, using riemannian foliation theory, we classify compact radiant Sim(n-1,1) affine manifolds M such that D(M') the image of the universal cover M' of M by the developing map D is contained in the upper cone defined q
Keywords
Cite
@article{arxiv.math/0207063,
title = {Closed similarity lorentzian affine manifolds},
author = {A. Tsemo},
journal= {arXiv preprint arXiv:math/0207063},
year = {2007}
}
Comments
9 pages, 12 references