**Beiträge zur Algebra und Geometrie
**

Contributions to Algebra and Geometry

Vol. 39, No. 1, pp. 169-179 (1998)

#
Spherical Hypersurfaces with 2-Type Gauss Map

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Bang-yen Chen; Shi-jie Li

Department of Mathematics, Michigan State University

East Lansing, Michigan 48824-1027, USA

e-mail: bychen@math.msu.edu
Department of Mathematics, South China Normal University

Guangzhou 510631, China

e-mail: lisj@scnu.edu.cn

**Abstract:** B. Y. Chen and P. Piccinni proved in [7] that spherical hypersurfaces have 1-type Gauss map if and only if they have constant mean curvature and constant scalar curvature. Moreover, they proved that there exists a codimension 2 compact spherical Einstein submanifold which has 2-type Gauss map and which also has constant mean curvature and constant length of second fundamental form. In contrast, we prove in this article that every compact spherical hypersurface with 2-type Gauss map is non-Einsteinian and has non-constant mean curvature and non-constant length of second fundamental form.

**Keywords:** spherical hypersurface; 2-type Gauss map; non-constant mean curvature

**Classification (MSC91):** 53C4053C42

**Full text of the article:**

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