具有规定光学几何的洛伦兹流形的 Levi-Civita 连接

Cubo (Temuco) Pub Date : 2024-07-09 DOI:10.56754/0719-0646.2602.239

D. Alekseevsky, Masoud Ganji, Gerd Schmalz, Andrea Spiro

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引用次数: 1

摘要

我们明确地推导了洛伦兹流形 \((M,g)\)的列维-奇维塔连接的克里斯托弗符号，该流形具有凯勒-萨崎类型的规定光学几何。本文发现的公式有几个重要的应用，如确定具有规定光学几何的洛伦兹流形的几何不变式或解决曲率约束。

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The Levi-Civita connections of Lorentzian manifolds with prescribed optical geometries

We explicitly derive the Christoffel symbols in terms of adapted frame fields for the Levi-Civita connection of a Lorentzian \(n\)-manifold \((M, g)\), equipped with a prescribed optical geometry of Kähler-Sasaki type. The formulas found in this paper have several important applications, such as determining the geometric invariants of Lorentzian manifolds with prescribed optical geometries or solving curvature constraints.

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Cubo (Temuco)

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