Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
Differential Geometry
2026-04-16 v2
Abstract
In this paper, we study the geometry and topology of complete gradient shrinking Sasaki-Ricci solitons. We first prove that they must be connected at infinity. This is a Sasaki analogue of gradient shrinking K\"ahler-Ricci solitons. Secondly, with the positive sectional curvature or positive transverse holomorphic bisectional curvature, we show that they must be compact. All results are served as a generalization of Perelman in dimension three, of Naber in dimension four, and of Munteanu-Wang in all dimensions, respectively.
Keywords
Cite
@article{arxiv.2508.13495,
title = {Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons},
author = {Shu-Cheng Chang and Yingbo Han and Chin-Tung Wu},
journal= {arXiv preprint arXiv:2508.13495},
year = {2026}
}