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

Bang-yen Chen; Shi-jie Li

Department of Mathematics, Michigan State University
East Lansing, Michigan 48824-1027, USA

Department of Mathematics, South China Normal University
Guangzhou 510631, China

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

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