GOLDEN- AND PRODUCT-SHAPED HYPERSURFACES IN REAL SPACE FORMS
GOLDEN- AND PRODUCT-SHAPED HYPERSURFACES IN REAL SPACE FORMS
复制标题
DOI：
10.1142/s0219887813200065
复制
发表时间：
2013-03
影响因子：
1.8
通讯作者：
M. Crășmăreanu;C. Hretcanu;M. Munteanu
中科院分区：
文献类型：
--
作者：
M. Crășmăreanu;C. Hretcanu;M. Munteanu
我们通过设定形状算子为黄金型或乘积型，分别在实空间形式中定义了两类超曲面，即黄金形状的和乘积形状的。基于等参超曲面的分类，我们得到上述超曲面的整个族如下：在黄金型的情形中，所有的都是超球面、一个双曲空间以及一个广义的克利福德环面，而对于乘积型的情形，根据周围空间形式的类型，即分别为抛物型、双曲型或椭圆型，我们分别得到单位超球面、超平面、一个超球面以及与其相关的克利福德环面。
We define two classes of hypersurfaces in real space forms, golden- and product-shaped, respectively, by imposing the shape operator to be of golden or product type. We obtain the whole families of above hypersurfaces, based on the classification of isoparametric hypersurfaces, as follows: in the golden case all are hyperspheres, a hyperbolic space and a generalized Clifford torus, while for the product case we obtain the unit hypersphere, the hyperplane, a hypersphere and its associated Clifford torus, respectively, according to the type of the ambient space form namely parabolic, hyperbolic or elliptic, respectively.