Three-dimensional conformally symmetric manifolds
E. Calvi\~no-Louzao, E. Garc\'ia-R\'io, J. Seoane-Bascoy, R., V\'azquez-Lorenzo
TL;DR
This paper investigates conformally symmetric manifolds in three dimensions, proving their non-existence in Riemannian cases and classifying them locally in Lorentzian cases, including analysis of their isometry classes.
Contribution
It establishes the non-existence of non-trivial conformally symmetric manifolds in 3D Riemannian geometry and provides a complete local classification in Lorentzian signature.
Findings
No non-trivial conformally symmetric 3D Riemannian manifolds exist.
Complete local classification of conformally symmetric Lorentzian 3D manifolds.
Analysis of isometry classes of these manifolds.
Abstract
The non-existence of non-trivial conformally symmetric manifolds in the three-dimensional Riemannian setting is shown. In Lorentzian signature, a complete local classification is obtained. Furthermore, the isometry classes are examined.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds