Warped product rigidity
Differential Geometry
2013-02-05 v2
Abstract
In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvature of a warped product manifold over a fixed base. As an application, this warped product structure will be used to study warped product Einstein structures in "Uniqueness of warped product Einstein metrics and applications".
Cite
@article{arxiv.1110.2455,
title = {Warped product rigidity},
author = {Chenxu He and Peter Petersen and William Wylie},
journal= {arXiv preprint arXiv:1110.2455},
year = {2013}
}
Comments
34 pages. This version contains new applications about how Ricci and scalar curvatures determine warped products