English

Rigidity and Non-Rigidity of $\mathbb{H}^n/\mathbb{Z}^{n-2}$ with Scalar Curvature Bounded from Below

Differential Geometry 2023-11-02 v2

Abstract

We show that the hyperbolic manifold Hn/Zn2\mathbb{H}^n/\mathbb{Z}^{n-2} is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound n(n1)-n(n-1), and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results.

Keywords

Cite

@article{arxiv.2303.15752,
  title  = {Rigidity and Non-Rigidity of $\mathbb{H}^n/\mathbb{Z}^{n-2}$ with Scalar Curvature Bounded from Below},
  author = {Tianze Hao and Yuhao Hu and Peng Liu and Yuguang Shi},
  journal= {arXiv preprint arXiv:2303.15752},
  year   = {2023}
}