In recent decades, there has been an increase in the number of publications related to the hypersurfaces of real space forms with two principal curvatures. The works focus mainly on the case when one of the two principal curvatures is simple. The purpose of this paper is to study a slightly more general class of complete minimal hypersurfaces in real space forms of constant curvature c, namely those with $$\mathrm{n}-1$$ principal curvatures having the same sign everywhere. From assumptions on the scalar curvature R and the Gauss–Kronecker curvature K we characterize Clifford tori if $$c > 0$$ and prove that K is identically zero if $$c \le 0$$ .

中文翻译：

---

关于空间形式的完全最小超曲面的主曲率

近几十年来，与具有两个主曲率的实空间形式的超曲面相关的出版物数量有所增加。工作主要集中在两个主曲率之一是简单的情况。本文的目的是研究一类稍微更一般的完全最小超曲面，在实空间形式的常曲率 c 中，即具有 $$\mathrm{n}-1$$ 主曲率处处具有相同符号的那些。根据对标量曲率 R 和 Gauss-Kronecker 曲率 K 的假设，我们在 $$c > 0$$ 时刻画 Clifford tori 并证明如果 $$c \le 0$$ 则 K 完全为零。