Embedded constant mean curvature hypertori in the $2n$-sphere

Brendle proved Lawson conjecture about minimal embedded torus in the round three-dimensional sphere. Carlotto and Schulz constructed a minimal embedded three-dimensional hypertorus in the round four-dimensional sphere and conjectured that their hypertorus is a unique minimal embedded three-dimensional hypertorus in the round four-dimensional sphere. In this paper, we construct two different constant mean curvature embedded $(2n-1)$-dimensional hypertori (that is, topological type ${\mathbb{S}}^{n-1}\times {\mathbb{S}}^{n-1}\times {\mathbb{S}}^1$) which have the same negative mean curvature $H$ in the round $2n$-dimensional sphere ${\mathbb{S}}^{2n}(1)$ .