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Publishing Language: Chinese | Open Access

Some rigidity theorems for closed Ricci shrinkers

Wenyan YUE1, Shijin ZHANG2( )
School of Mathematical Sciences, Capital Normal University, Beijing 100048
School of Mathematical Sciences, Beihang University, Beijing 102206
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Abstract

This paper study some properties about the shrinking gradient Ricci solitons on closed manifold, under the assumptions of L n / 2 -norm of traceless curvature tensor are sufficiently small and the diameter has an upper bound and the volume has a lower bound, using the classical Moser iteration to give some rigidity results, such as without assumption of volume has a lower bound if the dimension is 4.

Keywords

shrinking gradient Ricci solitonstraceless curvature tensorspherical space form
CLC number: O186 Document code: A

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Journal of Capital Normal University (Natural Science Edition)
Volume 47 Issue 1,
February 2026
Pages 14-20
DOI: 10.19789/j.1004-9398.2026.01.002

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YUE W, ZHANG S. Some rigidity theorems for closed Ricci shrinkers. Journal of Capital Normal University (Natural Science Edition), 2026, 47(1): 14-20. https://doi.org/10.19789/j.1004-9398.2026.01.002

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Received: 10 March 2025
Published: 01 February 2026
© The editorial department of Journal of Capital Normal University (Natural Science Edition) 2025.

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).