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In this paper, we prove that minimal hypersurfaces when $n\geq 3$ and nonzeroconstant mean curvature hypersurfaces when $n\geq2$ foliated by spheres inparallel horizontal hyperplanes in ${\mathbb{H}}^n \times \mathbb{R}$ must berotationally symmetric.

Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces