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

Tianze Hao   ; Yuhao Hu   ; Peng Liu   ; Yuguang Shi

Symmetry, integrability and geometry: methods and applications, Tome 19 (2023)

Résumé

We show that the hyperbolic manifold $\mathbb{H}^n/\mathbb{Z}^{n-2}$ 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 splitting results.

Détail

Keywords: scalar curvature, rigidity, ALH manifolds, $\mu$-bubbles.

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