Conformal flatness of compact three-dimensional Cotton-parallel manifolds
Differential Geometry
2023-10-17 v2
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.
Cite
@article{arxiv.2301.06700,
title = {Conformal flatness of compact three-dimensional Cotton-parallel manifolds},
author = {Ivo Terek},
journal= {arXiv preprint arXiv:2301.06700},
year = {2023}
}
Comments
Fixed a typo and updated a reference; this is the last author-produced version before publication