Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SPHERICAL SUBMANIFOLDS WITH FINITE TYPE SPHERICAL GAUSS MAP

  • Chen, Bang-Yen (Department of Mathematics Michigan State University) ;
  • Lue, Huei-Shyong (Department of Computer Sciences and Information Engineering Yuanpei Institute of Science and Technology Hsinchu)
  • Published : 2007.03.31
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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 $S^{n+1}$ 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.

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References

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  4. Classification of surfaces in a pseudo-sphere with 2-type pseudo-spherical Gauss map 2017, https://doi.org/10.1002/mana.201600498
  5. Hyperbolic submanifolds with finite type hyperbolic Gauss map vol.26, pp.02, 2015, https://doi.org/10.1142/S0129167X15500147
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