SPHERICAL SUBMANIFOLDS WITH FINITE TYPE SPHERICAL GAUSS MAP

- Journal title : Journal of the Korean Mathematical Society
- Volume 44, Issue 2, 2007, pp.407-442
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2007.44.2.407

Title & Authors

SPHERICAL SUBMANIFOLDS WITH FINITE TYPE SPHERICAL GAUSS MAP

Chen, Bang-Yen; Lue, Huei-Shyong;

Chen, Bang-Yen; Lue, Huei-Shyong;

Abstract

The study of Euclidean submanifolds with finite type "classical" Gauss map was initiated by B.-Y. Chen and P. Piccinni in [11]. On the other hand, it was believed that for spherical sub manifolds the concept of spherical Gauss map is more relevant than the classical one (see [20]). Thus the purpose of this article is to initiate the study of spherical submanifolds with finite type spherical Gauss map. We obtain several fundamental results in this respect. In particular, spherical submanifolds with 1-type spherical Gauss map are classified. From which we conclude that all isoparametric hypersurfaces of have 1-type spherical Gauss map. Among others, we also prove that Veronese surface and equilateral minimal torus are the only minimal spherical surfaces with 2-type spherical Gauss map.

Keywords

spherical Gauss map;finite type map;Clifford minimal torus;Veronese surface;equilateral torus;

Language

English

Cited by

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