The metric structure of compact rank-one ECS manifolds

Pseudo-Riemannian manifolds with nonzero parallel Weyl tensor which are not locally symmetric are known as ECS manifolds. Every ECS manifold carries a distinguished null parallel distribution D , the rank d ∈ { 1 , 2 } of which is referred to as the rank of the manifold itself. Under a natural gener...

Full description

Saved in:
Bibliographic Details
Published in:Annals of global analysis and geometry 2023-11, Vol.64 (4), p.24, Article 24
Main Authors: Derdzinski, Andrzej, Terek, Ivo
Format: Article
Language:English
Subjects:
Analysis
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Manifolds (mathematics)
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Ordinary differential equations
Riemann manifold
Tensors
Theorems
Vector space
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Pseudo-Riemannian manifolds with nonzero parallel Weyl tensor which are not locally symmetric are known as ECS manifolds. Every ECS manifold carries a distinguished null parallel distribution D , the rank d ∈ { 1 , 2 } of which is referred to as the rank of the manifold itself. Under a natural genericity assumption on the Weyl tensor, we fully describe the universal coverings of compact rank-one ECS manifolds. We then show that any generic compact rank-one ECS manifold must be translational , in the sense that the holonomy group of the natural flat connection induced on D is either trivial or isomorphic to Z 2 . We also prove that all four-dimensional rank-one ECS manifolds are noncompact, this time without having to assume genericity, as it is always the case in dimension four.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-023-09929-6