On spherical submanifolds with finite type spherical Gauss map
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CitationBektas, B., & Dursun, U. (2016). On spherical submanifolds with finite type spherical gauss map. Advances in Geometry, 16(2), 243-251. doi:10.1515/advgeom-2016-0005
Chen and Lue (2007) initiated the study of spherical submanifolds with finite type spherical Gauss map. In this paper, we firstly prove that a submanifold Mn of the unit sphere double-struck Sm-1 has non-mass-symmetric 1-type spherical Gauss map if and only if Mn is an open part of a small n-sphere of a totally geodesic (n + 1)-sphere double-struck Sn+1 ⊂ double-struck Sm-1. Then we show that a non-totally umbilical hypersurface M of double-struck Sn+1 with nonzero constant mean curvature in double-struck Sn+1 has mass-symmetric 2-type spherical Gauss map if and only if the scalar curvature curvature of M is constant. Finally, we classify constant mean curvature surfaces in double-struck S3 with mass-symmetric 2-type spherical Gauss map.
SourceAdvances in Geometry
Advances in Geometry