Dimension Reduction for Positively Curved Steady Solitons
Differential Geometry
2023-10-24 v1
Abstract
We consider noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature. We show that such solitons always dimension reduce at infinity. This generalizes an earlier result in [CDM22] to higher dimensions. In dimension four, we classify possible reductions at infinity, which lays foundation for possible classifications of steady solitons. Moreover, we show that any tangent flow at infinity of a general noncollapsed steady soliton must split off a line. This generalizes an earlier result in [BCDMZ21] to higher dimensions. While this article is under preparation, we realized that part of our main results are proved independently in a recent post [ZZ23] under different assumptions.
Keywords
Cite
@article{arxiv.2310.14020,
title = {Dimension Reduction for Positively Curved Steady Solitons},
author = {Pak-Yeung Chan and Zilu Ma and Yongjia Zhang},
journal= {arXiv preprint arXiv:2310.14020},
year = {2023}
}