We investigate projective properties of Lorentzian surfaces. In particular, we prove that if T is a non-flat torus, then the index of its isometry group in its projective group is at most two. We also prove that any topologically finite non-compact surface can be endowed with a metric having a non-isometric projective transformation of infinite order.

中文翻译：

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洛伦兹曲面的投影性质

我们研究洛伦兹曲面的投影特性。特别地，我们证明如果吨是非平环面，则其等距群在其射影群中的指数最多为二。我们还证明了任何拓扑有限的非紧曲面都可以被赋予具有无限阶的非等距射影变换的度量。