Geometric and analytic results for Einstein solitons
Differential Geometry
2024-04-12 v4
Abstract
We compute a lower bound for the scalar curvature of a gradient Einstein soliton under a certain assumption on its potential function. We establish an asymptotic behavior of the potential function on a noncompact gradient shrinking Einstein soliton. As a result, we obtain the finiteness of its fundamental group and its weighted volume. We also prove some geometric and analytic results for constructing gradient Einstein solitons that are realized as warped metrics, and we give a few explicit examples.
Cite
@article{arxiv.2208.01025,
title = {Geometric and analytic results for Einstein solitons},
author = {Enrique Fernando López Agila and José Nazareno Vieira Gomes},
journal= {arXiv preprint arXiv:2208.01025},
year = {2024}
}
Comments
Final version which has been accepted for publication in Mathematische Nachrichten