Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below
We show that the hyperbolic manifold ℍⁿ/ℤⁿ⁻² is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound −( − 1), and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related split...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212048 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below. Tianze Hao, Yuhao Hu, Peng Liu and Yuguang Shi. SIGMA 19 (2023), 083, 28 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862626999820877824 |
|---|---|
| author | Hao, Tianze Hu, Yuhao Liu, Peng Shi, Yuguang |
| author_facet | Hao, Tianze Hu, Yuhao Liu, Peng Shi, Yuguang |
| citation_txt | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below. Tianze Hao, Yuhao Hu, Peng Liu and Yuguang Shi. SIGMA 19 (2023), 083, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that the hyperbolic manifold ℍⁿ/ℤⁿ⁻² is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound −( − 1), and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results.
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| first_indexed | 2026-03-14T16:09:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212048 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T16:09:59Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hao, Tianze Hu, Yuhao Liu, Peng Shi, Yuguang 2026-01-23T10:12:41Z 2023 Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below. Tianze Hao, Yuhao Hu, Peng Liu and Yuguang Shi. SIGMA 19 (2023), 083, 28 pages 1815-0659 2020 Mathematics Subject Classification: 53C21; 53C24 arXiv:2303.15752 https://nasplib.isofts.kiev.ua/handle/123456789/212048 https://doi.org/10.3842/SIGMA.2023.083 We show that the hyperbolic manifold ℍⁿ/ℤⁿ⁻² is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound −( − 1), and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results. We thank Shihang He for kindly sharing his proof of Lemma B.1. We also thank the anonymous referees for carefully reading the manuscript and offering suggestions, which have led to improved exposition and a more direct argument now included in Remark 4.4. Research leading to this work was supported by the National Key R&D Program of China Grant 2020YFA0712800 (T. Hao, P. Liu, and Y. Shi) and the China Postdoctoral Science Foundation Grant 2021TQ0014 (Y. Hu). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below Article published earlier |
| spellingShingle | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below Hao, Tianze Hu, Yuhao Liu, Peng Shi, Yuguang |
| title | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below |
| title_full | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below |
| title_fullStr | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below |
| title_full_unstemmed | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below |
| title_short | Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below |
| title_sort | rigidity and non-rigidity of ℍⁿ/ℤⁿ⁻² with scalar curvature bounded from below |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212048 |
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