Asset Details
Do you wish to reserve the book?
The topology of compact rank-one ECS manifolds
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
The topology of compact rank-one ECS manifolds
Do you wish to request the book?
The topology of compact rank-one ECS manifolds
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
The topology of compact rank-one ECS manifolds
2023
Overview
Pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric, also known as essentially conformally symmetric (ECS) manifolds, have a natural local invariant, the rank, which equals 1 or 2, and is the rank of a certain distinguished null parallel distribution $\\mathcal{D}$. All known examples of compact ECS manifolds are of rank one and have dimensions greater than 4. We prove that a compact rank-one ECS manifold, if not locally homogeneous, replaced when necessary by a twofold isometric covering, must be a bundle over the circle with leaves of $\\mathcal{D}^\\perp$ serving as the fibres. The same conclusion holds in the locally homogeneous case if one assumes that $\\,\\mathcal{D}^\\perp$ has at least one compact leaf. We also show that in the pseudo-Riemannian universal covering space of any compact rank-one ECS manifold, the leaves of $\\mathcal{D}^\\perp$ are the factor manifolds of a global product decomposition.
Publisher
Cambridge University Press
Subject
