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arXiv · 2310.10938

The Levi-Civita connections of manifolds with prescribed optical geometries

Dmitri V. Alekseevsky·Masoud Ganji·Gerd Schmalz·Andrea Spiro
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Abstract

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 K\"ahler-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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Dmitri V. Alekseevsky, Masoud Ganji, Gerd Schmalz, Andrea Spiro. 2023-10-17. The Levi-Civita connections of manifolds with prescribed optical geometries. https://arxiv.org/abs/2310.10938

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