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arXiv · 2211.01167

Null-projectability of Levi-Civita connections

Andrzej Derdzinski·Kirollos Masood
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Abstract

We study the natural property of projectability of a torsion-free connection along a foliation on the underlying manifold, which leads to a projected torsion-free connection on a local leaf space, focusing on projectability of Levi-Civita connections of pseudo-Riemannian metric along foliations tangent to null parallel distributions. For the neutral metric signature and mid-dimensional distributions, Afifi showed in 1954 that projectability of the Levi-Civita connection characterizes, locally, the case of Patterson and Walker's Riemann extension metrics. We extend this correspondence to null parallel distributions of any dimension, introducing a suitable generalization of Riemann extensions.

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Andrzej Derdzinski, Kirollos Masood. 2022-11-02. Null-projectability of Levi-Civita connections. https://doi.org/10.1007/s00025-023-01911-9

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