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

Abstract

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 splitting results.