Growth conditions for conformal transformations preserving Riemannian completeness
Differential Geometry
2012-09-21 v3
Abstract
For a complete Riemannian metric, a pointwise conformal transformation may lead to a complete or incomplete transformed Riemannian metric, depending on the behavior of the conformal factor. We establish conditions on the growth of the conformal factor towards the infinity of the Riemannian metric, such that the conformally transformed Riemannian metric remains complete.
Keywords
Cite
@article{arxiv.1202.5437,
title = {Growth conditions for conformal transformations preserving Riemannian completeness},
author = {A. Dirmeier},
journal= {arXiv preprint arXiv:1202.5437},
year = {2012}
}
Comments
6 pages. Changes to version 1: An error in the earlier version of the main theorem has been pointed out. Version 2 contains a rectified statement including subsequent corrections of the corollary and the example. Version 3 contains some minor corrections to Version 2