时空几何理论中erbacher型约简的可能性

IF 3 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Annals of Physics Pub Date : 2025-08-18 DOI:10.1016/j.aop.2025.170183

Daniel de la Fuente , Rafael M. Rubio , Jose Torrente-Teruel

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引用次数: 0

摘要

虽然已知Erbacher关于黎曼等距浸入空间形式的约化定理在半黎曼几何领域中成立，但这些假设不能转化为伽利略几何的非相对论性背景。本文在洛伦兹和洛伦兹框架下证明了一个erbach型约简结果：具有一定无穷小对称性的时空中任意不变方向观测者的世界线可以嵌入到具有伽利略或洛伦兹结构的三维全测地线子流形中。

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On the possibility of a Erbacher-type reduction in the geometric theory of spacetimes

Although Erbacher’s reduction Theorem on Riemannian isometric immersions in the space forms is known to hold in the realm of semi-Riemannian geometry, the hypotheses cannot be translated to the non-relativistic context of Galilean geometry. In this paper, we prove a Erbacher-type reduction result in both Lorentzian and Galilean frameworks: the worldline of any Unchanged Direction observer in a spacetime with certain infinitesimal symmetries can be embedded in a 3-dimensional totally geodesic submanifold with Galilean or Lorentzian structure.

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来源期刊

Annals of Physics 物理-物理：综合

CiteScore

5.30

自引率

3.30%

发文量

211

审稿时长

47 days

期刊介绍： Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.