On open manifolds admitting no complete metric with positive scalar curvature
Differential Geometry
2024-12-04 v2
Abstract
In this paper, we investigate the topological obstruction problem for positive scalar curvature and uniformly positive scalar curvature on open manifolds. We present a definition for open Schoen-Yau-Schick manifolds and prove that there is no complete metric with positive scalar curvature on these manifolds. Similarly, we define weak Schoen-Yau-Shick manifolds by analogy, which are expected to admit no complete metrics with uniformly positive scalar curvature.
Keywords
Cite
@article{arxiv.2404.01660,
title = {On open manifolds admitting no complete metric with positive scalar curvature},
author = {Yuguang Shi and Jian Wang and Runzhang Wu and Jintian Zhu},
journal= {arXiv preprint arXiv:2404.01660},
year = {2024}
}
Comments
27 pages, 3 figures, to appear at Annales de l'Institut Fourier. All comments are welcome!