SPHERICAL SUBMANIFOLDS WITH FINITE TYPE SPHERICAL GAUSS MAP

Title & Authors
SPHERICAL SUBMANIFOLDS WITH FINITE TYPE SPHERICAL GAUSS MAP
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 $\small{S^{n+1}}$ 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
1.
Pseudo-Spherical Submanifolds with 1-Type Pseudo-Spherical Gauss Map, Results in Mathematics, 2017, 71, 3-4, 867
2.
On Submanifolds with 2-Type Pseudo-Hyperbolic Gauss Map in Pseudo-Hyperbolic Space, Mediterranean Journal of Mathematics, 2017, 14, 1
3.
Hyperbolic submanifolds with finite type hyperbolic Gauss map, International Journal of Mathematics, 2015, 26, 02, 1550014
4.
Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map, Annals of Global Analysis and Geometry, 2017
5.
On Submanifolds of Pseudo-Hyperbolic Space with 1-Type Pseudo-Hyperbolic Gauss Map, Zurnal matematiceskoj fiziki, analiza, geometrii, 2016, 12, 4, 315
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