RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE

In this paper, we give a characterization of Clifford tori $S^1(\sqrt{\textstyle\frac{nr+2-n}{nr}})\times S^{n-1}(\sqrt{\frac{n-2}{nr}})$ and $S^m(a)\times S^{n-m}(\sqrt{1-a^2}) (2 \le m \le n - 2, 0 \lt a^2 \lt 1)$ in a unit sphere Sn+1 (1). Our results extend the results due to Cheng and Yau [4], and Wang and Xia [11].