Rigidity and Non-Rigidity of ℍⁿ/ℤⁿ⁻² with Scalar Curvature Bounded from Below

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Hao, Tianze, Hu, Yuhao, Liu, Peng, Shi, Yuguang
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212048
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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

We show that the hyperbolic manifold ℍⁿ/ℤⁿ⁻² is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound −𝑛(𝑛 − 1), and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related spl...