Conformal flatness of compact three-dimensional Cotton-parallel manifolds

Ivo Terek

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arXiv · 2301.06700

Conformal flatness of compact three-dimensional Cotton-parallel manifolds

Ivo Terek

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Abstract

A three-dimensional pseudo-Riemannian manifold is called essentially conformally symmetric (ECS) if its Cotton tensor is parallel but nowhere-vanishing. In this note we prove that three-dimensional ECS manifolds must be noncompact or, equivalently, that every compact three-dimensional Cotton-parallel pseudo-Riemannian manifold must be conformally flat.

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Ivo Terek. 2023-01-17. Conformal flatness of compact three-dimensional Cotton-parallel manifolds. https://arxiv.org/abs/2301.06700

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