具有杀戮场的洛伦兹曲面的共形类

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-05 DOI:10.1112/blms.70010

Pierre Mounoud

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引用次数: 0

摘要

研究了具有（非零）杀戮场的二维洛伦兹环面共形类。我们定义了一个映射，将圆上的向量场（直到一个标量因子）关联到这样一个类。这个图不是内射的，而是有有限维的纤维。它允许我们刻画具有杀戮域的环面共形类，满足Mehidi给出的共轭点存在的条件。

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Conformal classes of Lorentzian surfaces with Killing fields

We study the conformal classes of two-dimensional Lorentzian tori with (nonzero) Killing fields. We define a map that associate to such a class a vector field on the circle (up to a scalar factor). This map is not injective but has finite-dimensional fiber. It allows us to characterize the conformal classes of tori with Killing field satisfying a condition related to the existence of conjugate points given by Mehidi.

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