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Four-dimensional shrinkers with pinched curvatures
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.
Related
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BibTeX
@misc{cao2026fourdimensional,
title = {{Four-dimensional shrinkers with pinched curvatures}},
author = {Xiaodong Cao and Jia-Yong Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11040},
eprint = {2610.11040},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11040},
}
RIS
TY - UNPB
TI - Four-dimensional shrinkers with pinched curvatures
AU - Xiaodong Cao
AU - Jia-Yong Wu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11040
UR - https://arxiv.org/abs/2610.11040
AB - 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.
ER -