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Closed similarity lorentzian affine manifolds

A. Tsemo
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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

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A. Tsemo. 2002-07-06. Closed similarity lorentzian affine manifolds. https://arxiv.org/abs/math/0207063

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