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Abstract
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 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 Sn+1 . Sm−1. Thenwe show that a non-totally umbilical hypersurfaceM of Sn+1 with nonzero constant mean curvature in 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 S3 with mass-symmetric 2-type spherical Gauss map.
Received: 2014-9-12
Published Online: 2016-4-16
Published in Print: 2016-4-1
© 2016 by Walter de Gruyter Berlin/Boston
