Uniqueness of static decompositions
Differential Geometry
2014-07-24 v2
Abstract
We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warping function satisfies severe restrictions, leading us to our classification results. Moreover, we show that certain condition on the lightlike sectional curvature ensures the uniqueness of static decomposition for Lorentzian manifolds.
Cite
@article{arxiv.0910.4933,
title = {Uniqueness of static decompositions},
author = {Manuel Gutiérrez and Benjamín Olea},
journal= {arXiv preprint arXiv:0910.4933},
year = {2014}
}
Comments
14 pages