Year: 2026
Type: preprint
Abstract: In this paper, we first classify complete four-dimensional shrinkers under a pinching condition on the $2$nd-Ricci curvature. We then classify closed four-dimensional shrinkers with (weighted) integral parameter-pinching of the half Weyl curvature under several pinching assumptions on the biorthogonal curvature. Finally, we establish a Hitchin-Thorpe type inequality for closed non-trivial four-dimensional shrinkers under some assumptions on the half Weyl curvature and the biorthogonal curvature.
Source: arXiv (Cornell University)
Authors: Cao, Xiaodong, Wu, Jia-Yong
Institutions: Shanghai University, Cornell University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G81950098
OpenAlex ID: W7221067229